Simplify

Problem 2701

(a) $\log _{4}(0.125)$ (Simplify your answers completely.) $\square$ (b) $\ln \left(e^{3}\right)$ $\square$ (c) $\ln (1 / e)$ $\square$

See Solution

Problem 2702

$23)\left(3 a^{2} b^{6}\right)^{2}\left(3 a^{10} b^{4}\right)^{3}$

See Solution

Problem 2703

Multiply. Write your answer in $\sqrt{3}(-8+\sqrt{5})$

See Solution

Problem 2704

Multiply. Write your answer as a fraction in simplest form. $\frac{7}{8} \times \frac{10}{3}$

See Solution

Problem 2705

ultiply. Write your answer in simplest form. $(-10-\sqrt{3})(3+\sqrt{22})$

See Solution

Problem 2706

Simplify $\sqrt{-45}$ . Write your answer as the product of a real number and $i$ . A. $5 \sqrt{3} i$ B. $-5 \sqrt{3} i$ C. $-3 \sqrt{5} i$ D. $3 \sqrt{5} i$ E. $\sqrt{45} i$

See Solution

Problem 2707

Write the following expression in terms of $i$ , perform multiplication, and simplify $\sqrt{-9} \sqrt{-27}$
Answer: $\square$ Preview My Answers Submit Answers

See Solution

Problem 2708

Question
Factor completely: $x^{2}(x+10)-(x+10)$
Answer Attempt iout of 3

See Solution

Problem 2709

Factor completely: $4 x^{2}\left(x^{2}+5\right)-\left(x^{2}+5\right)$
Answer Attempt 1 out of 3

See Solution

Problem 2710

Factor completely: $(x+6)^{6}+(x+6)^{7}$
Answer Attempt 1 out of 3

See Solution

Problem 2711

\begin{tabular}{|l|l|l|l|} \hline i) $\sqrt{0.64}$ & J) $\sqrt{0.04}$ & K) $\sqrt{\frac{128}{242}}$ & L) $\sqrt{\frac{12}{243}}$ \\ \hline m) $\sqrt{\frac{50}{98}}$ & n) $\sqrt{\frac{841}{49}}$ & o) $\sqrt{\frac{147}{300}}$ & p) $\sqrt{\frac{961}{144}}$ \\ \hline \end{tabular}

See Solution

Problem 2712

Simplify. Rationalize the denominator. $\frac{8}{-2+\sqrt{5}}$

See Solution

Problem 2713

Simplify. Rationalize the denominator. $\frac{-7}{8-\sqrt{2}}$

See Solution

Problem 2714

o to Polynomials, Add \& Subtract Question 21 10.3.59 Points:
Write the following polynomial in descending powers of the variable and with no miss ig powers. $\begin{array}{l} 8 x^{2}-67 \\ 8 x^{2}-67= \end{array}$ $\square$

See Solution

Problem 2715

(2) Simplify. Leave answers in simplest form using positive exponents in the final answer. a. $5^{19} \div 5^{-5}$ b. $\left(\frac{2}{3}\right)^{5} \cdot\left(\frac{4}{9}\right)^{-2}$

See Solution

Problem 2716

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. $\log \left(\frac{1000}{\sqrt{a^{2}+b^{2}}}\right)=$

See Solution

Problem 2717

$\left[{ }^{x}\right]$ Rewrite the following equatic $y+10=\frac{1}{7}(x+7)$

See Solution

Problem 2718

$y+6=-5(x-9)$

See Solution

Problem 2719

Complete the square and write the given equation in standard form. Then give the center and radius of the circle and graph the equation. $x^{2}+y^{2}+6 x+4 y+12=0$

See Solution

Problem 2720

Complete the square and write the given equation in standard form. Then give the center and radius of the circle and graph the equation. $x^{2}+y^{2}+6 x-4 y-12=0$

See Solution

Problem 2721

Write the following exponential equation in logarithmic form. Assume all variables are positive and not equal to one. $\begin{array}{l} 2^{c}=a \\ \log \mathrm{~b}(\mathrm{a})=\mathrm{c} \end{array}$

See Solution

Problem 2722

$3(4-1)-5(6+3)=$

See Solution

Problem 2723

Simplify $3 r+2 p-7 r+5$

See Solution

Problem 2724

Fully simplify $2 k+5-2 k+4 y$

See Solution

Problem 2725

Simplify $4 k+k+3$

See Solution

Problem 2726

$S D=\sqrt{0.81}$

See Solution

Problem 2727

Write the logarithmic equation as an exponential equation. $\log _{5}\left(\frac{1}{\sqrt{125}}\right)=-\frac{3}{2}$

See Solution

Problem 2728

2) semplifica l'espressione $\frac{\cos (\pi-\alpha) \sin \left(\frac{3 \pi}{2}+\alpha\right)}{\sin ^{2} \alpha} \tan (\alpha-\pi)+\tan \left(\frac{\pi}{2}+\alpha\right)$

See Solution

Problem 2729

$9 \sqrt{12}-4 \sqrt{27}=n \sqrt{3}$

See Solution

Problem 2730

2. Expand and simplify the following a) $2(3+x)+4 x$ b) $(x-3)(x+2)$ c) $(4 x-3)^{2}$

See Solution

Problem 2731

11. $32 \div\left(2^{3}-4\right)$

See Solution

Problem 2732

$4.3+(8.4-5.1)$

See Solution

Problem 2733

Properties of Logarithms - Example 4 Write each of the following as a single logarithm. (a) $3 \ln 2+\ln \left(x^{2}\right)=\ln 2^{3}+\ln \left(x^{2}\right)=\ln \left(8 x^{2}\right)$

See Solution

Problem 2734

Rewrite in simplest rational exponent form $\sqrt{x} \cdot \sqrt[4]{x}$ . Show each step of your process.

See Solution

Problem 2735

Rewrite in simplest radical form $\frac{x^{\frac{5}{6}}}{x^{\frac{1}{6}}}$ .Show each step of your process.

See Solution

Problem 2736

Simplify the expression. $\left(x^{\frac{1}{15}}\right)^{5}$

See Solution

Problem 2737

Rewrite the expression with rational exponents as a radical expression. $4 x^{\frac{3}{7}}$

See Solution

Problem 2738

$\sin \left(\frac{7 \pi}{2}+\alpha\right)+\cos (6 \pi-\alpha)+\tan \left(\frac{7 \pi}{2}+\alpha\right) \cos \left(\frac{3 \pi}{2}-\alpha\right)+\sin ^{2}\left(\frac{\pi}{2}+\alpha\right)+\sin ^{2}(-\alpha)$

See Solution

Problem 2739

Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $\sqrt{-77}$ $\square$ i $\square$ Submit

See Solution

Problem 2740

Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $-18+\sqrt{-5}$ $\square$ i $\sqrt{ }$ Submit

See Solution

Problem 2741

Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $\sqrt{-4}$ $\square$ i Submit

See Solution

Problem 2742

$4^{7}$

See Solution

Problem 2743

K. 1 Introduction to complex numbers 5 V
Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $16-\sqrt{-49}$

See Solution

Problem 2744

d) $\frac{\left(-3 a b^{-2}\right)^{5}}{\left(-9 a^{2} b^{-6}\right)^{2}}$

See Solution

Problem 2745

Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $\sqrt{-29}$ $\square$ i $\square$ Submit

See Solution

Problem 2746

the imagifry number $i$ to rewrite the expression below as a complex number. Simp radicers. - 2 Cr i $\square$
Submit

See Solution

Problem 2747

Factor by grouping. $x^{2}+6 x-9 x-54$ $(x+6)(x-3)$ $(x-6)(x-9)$ $2(3 x-27)$ $(x+6)(x-9)$

See Solution

Problem 2748

Stelle die Formel $f_{0}=\frac{60}{\sqrt{m^{\prime} \cdot d}}$ nach $d$ um.

See Solution

Problem 2749

Factor completely. $64 x^{2}-16$ $8\left(8 x^{2}-2\right)$ $16(2 x+1)(2 x-1)$ $4(4 x+2)(4 x-2)$ $8(8 x+2)(8 x-2)$

See Solution

Problem 2750

Use the Laws of Logarithms to combine the expression. $\log _{4}(2)+2 \log _{4}(9)$ $\square$ Need Help? Read It Master It Submit Answer

See Solution

Problem 2751

Convert $y=(x+3)^{2}-6$ to standard form. $y=x^{2}+$ $\square$ $x+$

See Solution

Problem 2752

(a) $\left(\frac{1}{5} \times \frac{2}{5}\right)+1 \frac{11}{25}$

See Solution

Problem 2753

Combine like terms to form an equivalent expression. $7+6 x+3 z-x-z-12$ $7+6 x+3 z-x-z-12=$ $\square$ (Simplify your answer.)

See Solution

Problem 2754

Bimplincaf. $\sqrt{15} \cdot \sqrt{3}$

See Solution

Problem 2755

Multiplicar. $\sqrt{3}(\sqrt{3}-6 \sqrt{14})$
Simplificar la respuesta tanto como sea posible. $\square$ $\sqrt{[ }$ $\square$

See Solution

Problem 2756

Hallar la pendiente $y$ la intersección con el eje $y$ de la recta. $-8 x+4 y=-12$
Escribir sus respuestas en su forma más simple. pendiente: $\square$ ㅁ Indefinido intersecclón con el eje $y$ : $\square$

See Solution

Problem 2757

Factorizar. $4 x^{2}-49$

See Solution

Problem 2758

Simplify the expression. $\frac{(z-8)(z+8)}{(z-8)}$ $\frac{(z-8)(z+8)}{(z-8)}=$ $\square$ (Simplify your answer.)

See Solution

Problem 2759

Factoring Quiz B Factor each completely. 1) $x^{2}+9 x$

See Solution

Problem 2760

Question 3 of 5
Subtract the following rational expressions $\frac{f+g}{16}-\frac{f-g}{16}$

See Solution

Problem 2761

Complete the square to re-write the quadratic function in vertex form: $y=x^{2}+4 x-9$

See Solution

Problem 2762

Use a rational exponent to write $\sqrt[3]{a^{4}}$ . $\sqrt[3]{a^{4}}=$

See Solution

Problem 2763

Complete the square to re-write the quadratic function in vertex form: $y=x^{2}-4 x+6$

See Solution

Problem 2764

Factor completely. $4 x^{2}+12 x-27$

See Solution

Problem 2765

Use identities to find an expression equivalent to $\frac{1+\sin (6 x)}{1-\sin (6 x)}-\frac{1-\sin (6 x)}{1+\sin (6 x)}$

See Solution

Problem 2766

Fully factorise $24 a^{2}-32 a$

See Solution

Problem 2767

Simplify. $\sqrt{12}+4 \sqrt{75}$

See Solution

Problem 2768

implify. $-2 \sqrt{18}+\sqrt{8}$

See Solution

Problem 2769

4) $\frac{320 \cdot 10^{-22}}{13 \cdot 10^{-21}-5 \cdot 10^{-21}}$

See Solution

Problem 2770

Multiply. $\sqrt{7}(8+\sqrt{3})$
Simplify your answer as much as possible.

See Solution

Problem 2771

Rationalize: $\quad \frac{11}{3 \sqrt{12}}$

See Solution

Problem 2772

Simplify. $\sqrt{v^{9}}$
Assume that the variable represents a positive real number.

See Solution

Problem 2773

Simplify. with an odd exponent $\sqrt{x^{13}}$
Assume that the variable represents a positive real number. $\square$ $\sqrt{\square}$

See Solution

Problem 2774

$\frac{a-\sqrt{a b}}{\sqrt{a b}} \cdot \frac{2}{b-\sqrt{a b}}$

See Solution

Problem 2775

Simplify the expression using synthetic division or the division algorithm. $\frac{\left(4 x^{2}-3 x-1\right)}{(2 x+5)}$

See Solution

Problem 2776

difference of radical expressions:...
Simplify. $\sqrt{50 x}+\sqrt{8 x}$
Assume that the variable represents a positive real number. $\square$

See Solution

Problem 2777

Simplify. $\sqrt{48} \times 3 \sqrt{27}$

See Solution

Problem 2778

Simplify. $2 \sqrt{20} \times \sqrt{18}$

See Solution

Problem 2779

Simplify. $\sqrt{27} \times 4 \sqrt{12}$

See Solution

Problem 2780

Multiply and simplify completely: $(4 x-3)(4 x-5)$

See Solution

Problem 2781

Multiply and add like terms: $(4 w+5)(4 w-5)$

See Solution

Problem 2782

$\frac{3x+15}{x^{2}-25}+\frac{4x^{2}-1}{2x^{2}+9x-5}$

See Solution

Problem 2783

$-2(-4+5)^{2}+2$

See Solution

Problem 2784

me that all variables repr c) $(8 \sqrt[3]{6})(2 \sqrt[3]{9})$

See Solution

Problem 2785

Nov 25 Exit Slip/HW - L3-6 Distributive Property
Use the distributive property to find an equivalent expression: $7(2 f-9)=$ $\square$
DO NOT USE ANY SPACES BETWEEN THE NUMBERS OR OPERATION SYMBOL

See Solution

Problem 2786

2. Estimate: $\qquad$ $\begin{array}{r} 673 \\ \times \quad 28 \\ \hline \end{array}$

See Solution

Problem 2787

Find an equivalent expression (use the "reverse" method) DO NOT TYPE SPACES $3 j-27=$ $\square$

See Solution

Problem 2788

$\left(6 x^{2}+3 x-5\right)-\left(2 x^{2}+6\right)$

See Solution

Problem 2789

Use the properties of logarithms to expand and simplify the expression. $\log _{10} \sqrt[3]{\frac{10+x}{100 x}}$

See Solution

Problem 2790

$\sin^2 \theta + \left(\cos^2 \theta\right)\left(\cos^2 \theta\right)$

See Solution

Problem 2791

$f(x)=x^{\frac{3}{2}} \text { and } g(x)=-2 x$ of 2: Find the formula for $\left(\frac{f}{g}\right)(x)$ and simplify your answer.

See Solution

Problem 2792

Fully factorise the expression $x^{2}-2 h x+h^{2}$

See Solution

Problem 2793

Fully factorise the expression $15 n^{2}-16 n p-15 p^{2}$

See Solution

Problem 2794

Simplify. $\sqrt{24 v^{11}}$
Assume that the variable represents a positive real number.

See Solution

Problem 2795

Simplify. $\sqrt{63 v^{3}}$
Assume that the variable represents a positive real number.

See Solution

Problem 2796

Factor by grouping. $\begin{array}{l} x^{3}+8 x^{2}+8 x+64 \\ x^{3}+8 x^{2}+8 x+64= \end{array}$

See Solution

Problem 2797

Simplify. $\sqrt{16 u^{7}}$
Assume that the variable represents a positive real number.

See Solution

Problem 2798

Square root addition or subtraction with three terms
Simplify. $2 \sqrt{27}+15 \sqrt{3}-\sqrt{12}$

See Solution

Problem 2799

Simplify. $\sqrt{45}+3 \sqrt{20}-12 \sqrt{5}$

See Solution

Problem 2800

Simplify. $13 \sqrt{2}-4 \sqrt{72}+\sqrt{32}$

See Solution

1 ...25 26 27 28 29 30 31 ...56

Simplify

Problem 2701

(a) log⁡4(0.125)\log _{4}(0.125)log4​(0.125) (Simplify your answers completely.) □\square□ (b) ln⁡(e3)\ln \left(e^{3}\right)ln(e3) □\square□ (c) ln⁡(1/e)\ln (1 / e)ln(1/e) □\square□

Problem 2702

23)(3a2b6)2(3a10b4)323)\left(3 a^{2} b^{6}\right)^{2}\left(3 a^{10} b^{4}\right)^{3}23)(3a2b6)2(3a10b4)3

Problem 2703

Multiply. Write your answer in 3(−8+5)\sqrt{3}(-8+\sqrt{5})3​(−8+5​)

Problem 2704

Multiply. Write your answer as a fraction in simplest form. 78×103\frac{7}{8} \times \frac{10}{3}87​×310​

Problem 2705

ultiply. Write your answer in simplest form. (−10−3)(3+22)(-10-\sqrt{3})(3+\sqrt{22})(−10−3​)(3+22​)

Problem 2706

Simplify −45\sqrt{-45}−45​. Write your answer as the product of a real number and iii. A. 53i5 \sqrt{3} i53​i B. −53i-5 \sqrt{3} i−53​i C. −35i-3 \sqrt{5} i−35​i D. 35i3 \sqrt{5} i35​i E. 45i\sqrt{45} i45​i

Problem 2707

Write the following expression in terms of iii, perform multiplication, and simplify −9−27\sqrt{-9} \sqrt{-27}−9​−27​Answer: □\square□ Preview My Answers Submit Answers

Problem 2708

QuestionFactor completely: x2(x+10)−(x+10)x^{2}(x+10)-(x+10)x2(x+10)−(x+10)Answer Attempt iout of 3

Problem 2709

Factor completely: 4x2(x2+5)−(x2+5)4 x^{2}\left(x^{2}+5\right)-\left(x^{2}+5\right)4x2(x2+5)−(x2+5)Answer Attempt 1 out of 3

Problem 2710

Factor completely: (x+6)6+(x+6)7(x+6)^{6}+(x+6)^{7}(x+6)6+(x+6)7Answer Attempt 1 out of 3

Problem 2711

Problem 2712

Simplify. Rationalize the denominator. 8−2+5\frac{8}{-2+\sqrt{5}}−2+5​8​

Problem 2713

Simplify. Rationalize the denominator. −78−2\frac{-7}{8-\sqrt{2}}8−2​−7​

Problem 2714

o to Polynomials, Add \& Subtract Question 21 10.3.59 Points:Write the following polynomial in descending powers of the variable and with no miss ig powers. 8x2−678x2−67=\begin{array}{l} 8 x^{2}-67 \\ 8 x^{2}-67= \end{array}8x2−678x2−67=​ □\square□

Problem 2715

(2) Simplify. Leave answers in simplest form using positive exponents in the final answer. a. 519÷5−55^{19} \div 5^{-5}519÷5−5 b. (23)5⋅(49)−2\left(\frac{2}{3}\right)^{5} \cdot\left(\frac{4}{9}\right)^{-2}(32​)5⋅(94​)−2

Problem 2716

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. log⁡(1000a2+b2)=\log \left(\frac{1000}{\sqrt{a^{2}+b^{2}}}\right)=log(a2+b2​1000​)=

Problem 2717

[x]\left[{ }^{x}\right][x] Rewrite the following equatic y+10=17(x+7)y+10=\frac{1}{7}(x+7)y+10=71​(x+7)

Problem 2718

y+6=−5(x−9)y+6=-5(x-9)y+6=−5(x−9)

Problem 2719

Complete the square and write the given equation in standard form. Then give the center and radius of the circle and graph the equation. x2+y2+6x+4y+12=0x^{2}+y^{2}+6 x+4 y+12=0x2+y2+6x+4y+12=0

Problem 2720

Complete the square and write the given equation in standard form. Then give the center and radius of the circle and graph the equation. x2+y2+6x−4y−12=0x^{2}+y^{2}+6 x-4 y-12=0x2+y2+6x−4y−12=0

Problem 2721

Write the following exponential equation in logarithmic form. Assume all variables are positive and not equal to one. 2c=alog⁡ b(a)=c\begin{array}{l} 2^{c}=a \\ \log \mathrm{~b}(\mathrm{a})=\mathrm{c} \end{array}2c=alog b(a)=c​

Problem 2722

3(4−1)−5(6+3)=3(4-1)-5(6+3)=3(4−1)−5(6+3)=

Problem 2723

Simplify 3r+2p−7r+53 r+2 p-7 r+53r+2p−7r+5

Problem 2724

Fully simplify 2k+5−2k+4y2 k+5-2 k+4 y2k+5−2k+4y

Problem 2725

Simplify 4k+k+34 k+k+34k+k+3

Problem 2726

SD=0.81S D=\sqrt{0.81}SD=0.81​

Problem 2727

Write the logarithmic equation as an exponential equation. log⁡5(1125)=−32\log _{5}\left(\frac{1}{\sqrt{125}}\right)=-\frac{3}{2}log5​(125​1​)=−23​

Problem 2728

Problem 2729

912−427=n39 \sqrt{12}-4 \sqrt{27}=n \sqrt{3}912​−427​=n3​

Problem 2730

2. Expand and simplify the following a) 2(3+x)+4x2(3+x)+4 x2(3+x)+4x b) (x−3)(x+2)(x-3)(x+2)(x−3)(x+2) c) (4x−3)2(4 x-3)^{2}(4x−3)2

Problem 2731

11. 32÷(23−4)32 \div\left(2^{3}-4\right)32÷(23−4)

Problem 2732

4.3+(8.4−5.1)4.3+(8.4-5.1)4.3+(8.4−5.1)

Problem 2733

Properties of Logarithms - Example 4 Write each of the following as a single logarithm. (a) 3ln⁡2+ln⁡(x2)=ln⁡23+ln⁡(x2)=ln⁡(8x2)3 \ln 2+\ln \left(x^{2}\right)=\ln 2^{3}+\ln \left(x^{2}\right)=\ln \left(8 x^{2}\right)3ln2+ln(x2)=ln23+ln(x2)=ln(8x2)

Problem 2734

Rewrite in simplest rational exponent form x⋅x4\sqrt{x} \cdot \sqrt[4]{x}x​⋅4x​. Show each step of your process.

Problem 2735

Rewrite in simplest radical form x56x16\frac{x^{\frac{5}{6}}}{x^{\frac{1}{6}}}x61​x65​​.Show each step of your process.

Problem 2736

Simplify the expression. (x115)5\left(x^{\frac{1}{15}}\right)^{5}(x151​)5

Problem 2737

Rewrite the expression with rational exponents as a radical expression. 4x374 x^{\frac{3}{7}}4x73​

Problem 2738

Problem 2739

Use the imaginary number iii to rewrite the expression below as a complex number. Simplify all radicals. −77\sqrt{-77}−77​ □\square□ i □\square□ Submit

Problem 2740

Use the imaginary number iii to rewrite the expression below as a complex number. Simplify all radicals. −18+−5-18+\sqrt{-5}−18+−5​ □\square□ i \sqrt{ }​ Submit

Problem 2741

Use the imaginary number iii to rewrite the expression below as a complex number. Simplify all radicals. −4\sqrt{-4}−4​ □\square□ i Submit

(a) $\log _{4}(0.125)$ (Simplify your answers completely.) $\square$ (b) $\ln \left(e^{3}\right)$ $\square$ (c) $\ln (1 / e)$ $\square$

$23)\left(3 a^{2} b^{6}\right)^{2}\left(3 a^{10} b^{4}\right)^{3}$

Multiply. Write your answer in $\sqrt{3}(-8+\sqrt{5})$

Multiply. Write your answer as a fraction in simplest form. $\frac{7}{8} \times \frac{10}{3}$

ultiply. Write your answer in simplest form. $(-10-\sqrt{3})(3+\sqrt{22})$

Simplify $\sqrt{-45}$ . Write your answer as the product of a real number and $i$ . A. $5 \sqrt{3} i$ B. $-5 \sqrt{3} i$ C. $-3 \sqrt{5} i$ D. $3 \sqrt{5} i$ E. $\sqrt{45} i$

Write the following expression in terms of $i$ , perform multiplication, and simplify $\sqrt{-9} \sqrt{-27}$
Answer: $\square$ Preview My Answers Submit Answers

Question
Factor completely: $x^{2}(x+10)-(x+10)$
Answer Attempt iout of 3

Factor completely: $4 x^{2}\left(x^{2}+5\right)-\left(x^{2}+5\right)$
Answer Attempt 1 out of 3

Factor completely: $(x+6)^{6}+(x+6)^{7}$
Answer Attempt 1 out of 3

Simplify. Rationalize the denominator. $\frac{8}{-2+\sqrt{5}}$

Simplify. Rationalize the denominator. $\frac{-7}{8-\sqrt{2}}$

o to Polynomials, Add \& Subtract Question 21 10.3.59 Points:
Write the following polynomial in descending powers of the variable and with no miss ig powers. $\begin{array}{l} 8 x^{2}-67 \\ 8 x^{2}-67= \end{array}$ $\square$

(2) Simplify. Leave answers in simplest form using positive exponents in the final answer. a. $5^{19} \div 5^{-5}$ b. $\left(\frac{2}{3}\right)^{5} \cdot\left(\frac{4}{9}\right)^{-2}$

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. $\log \left(\frac{1000}{\sqrt{a^{2}+b^{2}}}\right)=$

$\left[{ }^{x}\right]$ Rewrite the following equatic $y+10=\frac{1}{7}(x+7)$

$y+6=-5(x-9)$

Complete the square and write the given equation in standard form. Then give the center and radius of the circle and graph the equation. $x^{2}+y^{2}+6 x+4 y+12=0$

Complete the square and write the given equation in standard form. Then give the center and radius of the circle and graph the equation. $x^{2}+y^{2}+6 x-4 y-12=0$

Write the following exponential equation in logarithmic form. Assume all variables are positive and not equal to one. $\begin{array}{l} 2^{c}=a \\ \log \mathrm{~b}(\mathrm{a})=\mathrm{c} \end{array}$

$3(4-1)-5(6+3)=$

Simplify $3 r+2 p-7 r+5$

Fully simplify $2 k+5-2 k+4 y$

Simplify $4 k+k+3$

$S D=\sqrt{0.81}$

Write the logarithmic equation as an exponential equation. $\log _{5}\left(\frac{1}{\sqrt{125}}\right)=-\frac{3}{2}$

$9 \sqrt{12}-4 \sqrt{27}=n \sqrt{3}$

2. Expand and simplify the following a) $2(3+x)+4 x$ b) $(x-3)(x+2)$ c) $(4 x-3)^{2}$

11. $32 \div\left(2^{3}-4\right)$

$4.3+(8.4-5.1)$

Properties of Logarithms - Example 4 Write each of the following as a single logarithm. (a) $3 \ln 2+\ln \left(x^{2}\right)=\ln 2^{3}+\ln \left(x^{2}\right)=\ln \left(8 x^{2}\right)$

Rewrite in simplest rational exponent form $\sqrt{x} \cdot \sqrt[4]{x}$ . Show each step of your process.

Rewrite in simplest radical form $\frac{x^{\frac{5}{6}}}{x^{\frac{1}{6}}}$ .Show each step of your process.

Simplify the expression. $\left(x^{\frac{1}{15}}\right)^{5}$

Rewrite the expression with rational exponents as a radical expression. $4 x^{\frac{3}{7}}$

Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $\sqrt{-77}$ $\square$ i $\square$ Submit

Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $-18+\sqrt{-5}$ $\square$ i $\sqrt{ }$ Submit

Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $\sqrt{-4}$ $\square$ i Submit

$4^{7}$

K. 1 Introduction to complex numbers 5 V
Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $16-\sqrt{-49}$

d) $\frac{\left(-3 a b^{-2}\right)^{5}}{\left(-9 a^{2} b^{-6}\right)^{2}}$

Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $\sqrt{-29}$ $\square$ i $\square$ Submit

the imagifry number $i$ to rewrite the expression below as a complex number. Simp radicers. - 2 Cr i $\square$
Submit

Factor by grouping. $x^{2}+6 x-9 x-54$ $(x+6)(x-3)$ $(x-6)(x-9)$ $2(3 x-27)$ $(x+6)(x-9)$

Stelle die Formel $f_{0}=\frac{60}{\sqrt{m^{\prime} \cdot d}}$ nach $d$ um.

Factor completely. $64 x^{2}-16$ $8\left(8 x^{2}-2\right)$ $16(2 x+1)(2 x-1)$ $4(4 x+2)(4 x-2)$ $8(8 x+2)(8 x-2)$

Use the Laws of Logarithms to combine the expression. $\log _{4}(2)+2 \log _{4}(9)$ $\square$ Need Help? Read It Master It Submit Answer

Convert $y=(x+3)^{2}-6$ to standard form. $y=x^{2}+$ $\square$ $x+$

(a) $\left(\frac{1}{5} \times \frac{2}{5}\right)+1 \frac{11}{25}$

Combine like terms to form an equivalent expression. $7+6 x+3 z-x-z-12$ $7+6 x+3 z-x-z-12=$ $\square$ (Simplify your answer.)

Bimplincaf. $\sqrt{15} \cdot \sqrt{3}$

Multiplicar. $\sqrt{3}(\sqrt{3}-6 \sqrt{14})$
Simplificar la respuesta tanto como sea posible. $\square$ $\sqrt{[ }$ $\square$

Hallar la pendiente $y$ la intersección con el eje $y$ de la recta. $-8 x+4 y=-12$
Escribir sus respuestas en su forma más simple. pendiente: $\square$ ㅁ Indefinido intersecclón con el eje $y$ : $\square$

Factorizar. $4 x^{2}-49$

Simplify the expression. $\frac{(z-8)(z+8)}{(z-8)}$ $\frac{(z-8)(z+8)}{(z-8)}=$ $\square$ (Simplify your answer.)

Factoring Quiz B Factor each completely. 1) $x^{2}+9 x$

Question 3 of 5
Subtract the following rational expressions $\frac{f+g}{16}-\frac{f-g}{16}$

Complete the square to re-write the quadratic function in vertex form: $y=x^{2}+4 x-9$

Use a rational exponent to write $\sqrt[3]{a^{4}}$ . $\sqrt[3]{a^{4}}=$

Complete the square to re-write the quadratic function in vertex form: $y=x^{2}-4 x+6$

Factor completely. $4 x^{2}+12 x-27$

Use identities to find an expression equivalent to $\frac{1+\sin (6 x)}{1-\sin (6 x)}-\frac{1-\sin (6 x)}{1+\sin (6 x)}$

Fully factorise $24 a^{2}-32 a$

Simplify. $\sqrt{12}+4 \sqrt{75}$

implify. $-2 \sqrt{18}+\sqrt{8}$

4) $\frac{320 \cdot 10^{-22}}{13 \cdot 10^{-21}-5 \cdot 10^{-21}}$

Multiply. $\sqrt{7}(8+\sqrt{3})$
Simplify your answer as much as possible.

Rationalize: $\quad \frac{11}{3 \sqrt{12}}$

Simplify. $\sqrt{v^{9}}$
Assume that the variable represents a positive real number.

Simplify. with an odd exponent $\sqrt{x^{13}}$
Assume that the variable represents a positive real number. $\square$ $\sqrt{\square}$

$\frac{a-\sqrt{a b}}{\sqrt{a b}} \cdot \frac{2}{b-\sqrt{a b}}$