Math Statement

Problem 18201

Evaluate (1.28×105)+(1.13×103)(1.28 \times 10^{5}) + (1.13 \times 10^{3}) in scientific notation. Then, (7.26×106)(1.3×104)(7.26 \times 10^{6}) - (1.3 \times 10^{4}). Lastly, find the mass of 480,000,000480,000,000 bacteria if one bacterium has a mass of 2×10122 \times 10^{-12} gram.

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Problem 18202

Operate the functions: f(x)=x1f(x)=x-1, g(x)=x21g(x)=x^{2}-1, h(x)=3x22x1h(x)=3x^{2}-2x-1. Find (g+h)(x)(g+h)(x), (hf)(x)(h-f)(x), (fh)(x)(f-h)(x).

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Problem 18203

Solve for xx in the equation x52=9\frac{x}{5}-2=9.

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Problem 18204

Solve for xx: 5=x5+65=-\frac{x}{5}+6

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Problem 18205

Multiply: 4x2(3x22x3)=4 x^{2}(3 x^{2}-2 x-3)=

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Problem 18206

Simplify the expression: (9xy+3y4)(11y4+9x11xy)+(5y46xy)(9xy + 3y^4) - (11y^4 + 9x - 11xy) + (5y^4 - 6xy).

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Problem 18207

Weekly cost to make xx cars and yy trucks is C(x,y)=240,000+6,000x+4,000yC(x, y)=240,000+6,000x+4,000y. Find marginal costs and describe graphs.

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Problem 18208

Simplify the expression by rationalizing the denominator: 82\frac{8}{\sqrt{2}}.

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Problem 18209

Evaluate the function g(x,y,z)=ln(x+y+z)g(x, y, z)=\ln (x+y+z) for: (a) g(0,0,0)g(0,0,0), (b) g(1,0,0)g(1,0,0), (c) g(0,1,0)g(0,1,0), (d) g(z,x,y)g(z, x, y), (e) g(x+h,y+k,z+I)g(x+h, y+k, z+I).

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Problem 18210

Rationalize and simplify the expression: 1410\frac{\sqrt{14}}{\sqrt{10}}.

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Problem 18211

Simplify: 2y75v5+v227vy22 y \sqrt{75 v^{5}} + v^{2} \sqrt{27 v y^{2}} with y,v>0y, v > 0.

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Problem 18212

Solve for yy in the equation y+11+15=8\sqrt{y+11}+15=8. What is yy?

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Problem 18213

Which statements are true for all cc? I. limxcf(x)=0limxcf(x)=0\lim _{x \rightarrow c} f(x)=0 \Rightarrow \lim _{x \rightarrow c}|f(x)|=0. II. limxcf(x)=0limxcf(x)=0\lim _{x \rightarrow c}|f(x)|=0 \Rightarrow \lim _{x \rightarrow c} f(x)=0.

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Problem 18214

Solve (u+6)3+24=0(u+6)^{3}+24=0 for real uu and express your answer in simplified radical form.

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Problem 18215

Simplify the expression: 18x6y11\sqrt{18 x^{6} y^{11}}, assuming all variables are positive real numbers.

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Problem 18216

Determine the truth of these statements for all cc and LL: I. limxcf(x)=Llimxcf(x)=L\lim _{x \rightarrow c} f(x)=L \Rightarrow \lim _{x \rightarrow c}|f(x)|=|L|; II. limxcf(x)=Llimxcf(x)=L\lim _{x \rightarrow c}|f(x)|=|L| \Rightarrow \lim _{x \rightarrow c} f(x)=L.

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Problem 18217

Multiply: (5a7)(5a+7)=(5a - 7)(5a + 7) =

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Problem 18218

Multiply and simplify: (3782)(52+87)(3 \sqrt{7}-8 \sqrt{2})(5 \sqrt{2}+8 \sqrt{7}).

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Problem 18219

Solve these equations and verify your solutions:
1. 2(r+6)=4(r+4)2(r+6)=4(r+4)
2. 6(n+5)=3(n+16)6(n+5)=3(n+16)
3. 5(g+8)7=117g5(g+8)-7=117-g
4. 1245(x+15)=25x+612-\frac{4}{5}(x+15)=\frac{2}{5} x+6
5. 3(3m2)=2(3m+3)3(3 m-2)=2(3 m+3)

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Problem 18220

Simplify the expression: z35z43z15z^{-\frac{3}{5}} z^{\frac{4}{3}} z^{-\frac{1}{5}} using only positive exponents.

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Problem 18221

Write 144\sqrt[4]{14} as an exponential expression.

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Problem 18222

Find all values of aa where limxaf(x)\lim_{x \to a} f(x) exists for the piecewise function f(x)f(x) defined above.

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Problem 18223

Simplify the expression a4b2ab3\frac{a^{4} \cdot b^{2}}{a b^{3}}.

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Problem 18224

Simplify the expression: 2775\sqrt{\frac{27}{75}} and provide the answer in simplest form.

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Problem 18225

Find XZX Z given the equations XY=2x+1X Y=2 x+1 and YZ=5x44Y Z=5 x-44.

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Problem 18226

Simplify the expression: a3a2b4a2b3\frac{a^{3} \cdot a^{2} \cdot b^{4}}{a^{2} \cdot b^{3}}.

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Problem 18227

Multiply: (4x+5)2=(4x + 5)^{2} =

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Problem 18228

Determine if the limits L1=limx0+sin(πx)L_{1} = \lim _{x \rightarrow 0+} \sin(\frac{\pi}{x}) and L2=limx0sin(πx)L_{2} = \lim _{x \rightarrow 0-} \sin(\frac{\pi}{x}) exist.

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Problem 18229

Complete the multiplication pattern: 8×8=_8 \times 8 = \_ and 80×8=_80 \times 8 = \_

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Problem 18230

Find the missing numbers in the pattern:
4 × \_ = 32, 40 × \_ = 320, 400 × \_ = 3,200, 4,000 × \_ = 32,000, 40,000 × \_ = 320,000, 400,000 × \_ = 3,200,000, 4,000,000 × \_ = 32,000,000.

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Problem 18231

Calculate the value of 217\frac{\sqrt{21}}{7}.

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Problem 18232

Calculate: 800×8800 \times 8, 8,000×88,000 \times 8, 80,000×880,000 \times 8, 800,000×8800,000 \times 8, 8,000,000×88,000,000 \times 8.

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Problem 18233

Calculate 80×880 \times 8 and 800×8800 \times 8.

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Problem 18234

Apply the distributive property and simplify: 3(2x2)=-3(2 x-2) =

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Problem 18235

Multiply: (7x2)(3x2)=(-7 x^{2})(3 x^{2})=

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Problem 18236

Find the linear function ff given f(35)=12f\left(\frac{3}{5}\right)=\frac{1}{2} and f(2)=4f(2)=4: f(x)=52x1f(x)=\frac{5}{2}x-1.

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Problem 18237

Simplify the expression: ab6c12bc10\frac{a b^{6} c^{12}}{b c^{10}}.

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Problem 18238

Simplify and add: 22+272 \sqrt{2} + 2 \sqrt{7}. What is the result?

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Problem 18239

If two lines have slopes that are negative reciprocals, are they perpendicular? A. True B. False

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Problem 18240

Simplify the expression with positive exponents: (2a2b13a2b4)3=\left(\frac{2 a^{2} b^{1}}{3 a^{2} b^{4}}\right)^{3}=

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Problem 18241

Simplify the expression (2a2b13a2b4)3\left(\frac{2 a^{2} b^{1}}{3 a^{2} b^{4}}\right)^{3}.

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Problem 18242

Calculate: 22080=2 \sqrt{20} - \sqrt{80} =

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Problem 18243

Identify the parent function of the graph given by the equation y=4y=4.

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Problem 18244

Define E={vv<4}E=\{v \mid v<4\} and F={vv7}F=\{v \mid v \geq 7\}. Find EFE \cup F and EFE \cap F in interval notation.

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Problem 18245

Define sets A={xx1}A=\{x \mid x \geq 1\} and B={xx>6}B=\{x \mid x>6\}. Find ABA \cap B and ABA \cup B in interval notation.

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Problem 18246

Calculate the expression: 3322503 \sqrt{32}-2 \sqrt{50}.

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Problem 18247

Solve for xx: x+3=2x4x + 3 = 2x - 4. Find the value of xx.

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Problem 18248

Find the average velocity of a ball thrown upward on the moon, given y(t)=25t3t2y(t)=25t-3t^2, over the interval from 1 to 1+h1+h.

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Problem 18249

Find the union DED \cup E and intersection DED \cap E of the sets D={yy>4}D=\{y \mid y>4\} and E={yy5}E=\{y \mid y \leq 5\}.

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Problem 18250

Graph the system: {x+3y=3y=13x+1 \left\{\begin{array}{l} -x+3y=3 \\ y=\frac{1}{3}x+1 \end{array}\right. Provide the solution or state "No solution" or "Infinitely many".

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Problem 18251

Solve for qq in the equation: 21+q=8-21 + q = 8.

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Problem 18252

Solve for yy in the equation: 144=24y-144=-24 y.

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Problem 18253

Solve for yy: 6(y+4)5(y+5)=66(y+4) - 5(y+5) = -6 y= y =

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Problem 18254

Solve for cc in the equation c11=7c-11=-7.

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Problem 18255

Evaluate the functions: 1. (hg)(x)(h \circ g)(x) and 2. 2[f(gg)](x)2 \cdot [f \circ (g \circ g)](x), where g(x)=3x2g(x)=3x-2, f(x)=xf(x)=\sqrt{-x}, h(x)=3x+4h(x)=\frac{3}{x+4}.

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Problem 18256

Solve for aa: 50a2=200a50 a^{2} = 200 a. What is the value of aa?

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Problem 18257

Solve for aa in the equation: (a4)(a3)=2(a-4)(a-3)=2. What is the value of aa?
a= a=

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Problem 18258

A ball is thrown with a velocity of 40ft/s40 \mathrm{ft/s}. Find average velocity from t=2t=2 for (a) 0.5s, 0.05s, 0.1s, 0.01s and (b) instantaneous velocity at t=2t=2.

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Problem 18259

Rationalize the denominator of 4x+1\frac{4}{\sqrt{x}+1}.

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Problem 18260

Find the limit as xx approaches -1 for the expression x2+9x+88x+8\frac{x^{2}+9 x+8}{8 x+8}.

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Problem 18261

Solve for xx: 4x+2(4x+3)=184x + 2(4x + 3) = -18 x= x =

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Problem 18262

Find cc using the formula d=(rc)td=(r-c) t with d=18,r=9d=18, r=9, and t=3t=3. c=c=

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Problem 18263

Find the limit of f(x+h)f(x)h\frac{f(x+h)-f(x)}{h} for f(x)=x2+3x+2f(x)=x^{2}+3x+2, where h0h \neq 0. Simplify your answer.

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Problem 18264

Solve for xx in the equation: 3(x+1)4(x+3)=113(x+1)-4(x+3)=-11. Find x=x=

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Problem 18265

Find cc using the formula d=(rc)td=(r-c) t for d=26d=26, r=15r=15, and t=2t=2. c=c=

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Problem 18266

Solve the following equations: a. 5x6=05x - 6 = 0 b. 25x236=025x^2 - 36 = 0 c. 25x236=58925x^2 - 36 = 589 d. 25x236=60x7225x^2 - 36 = 60x - 72

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Problem 18267

Simplify the polynomial expression: 3(x+5)23(x+5)+63(x+5)^{2}-3(x+5)+6.

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Problem 18268

Simplify the polynomial expression: 2(x4)2+3(x4)+12(x-4)^{2}+3(x-4)+1.

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Problem 18269

Find the limit as xx approaches -8 for the expression x2644x+32\frac{x^{2}-64}{4 x+32}.

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Problem 18270

Expand (53x+4)2\left(\frac{5}{3} x+4\right)^{2} into a trinomial in simplest form.

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Problem 18271

Expand the expression to standard polynomial form: (x1)(x2+x+9)(x-1)(-x^{2}+x+9).

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Problem 18272

Expand (53x2)2\left(\frac{5}{3} x-2\right)^{2} into a trinomial in simplest form.

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Problem 18273

Solve for xx in the equation x413x2+36=0x^{4}-13x^{2}+36=0 and factor it if possible.

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Problem 18274

Factor the expression x412x2+32x^{4}-12 x^{2}+32.

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Problem 18275

Calculate (5)17=(-5)^{17}=

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Problem 18276

Calculate 4.313=4.3^{13}=

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Problem 18277

Expand the expression: (2x + 1)(x² - 5x - 7) to standard polynomial form.

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Problem 18278

Find the limit as xx approaches 5 for the expression x213x+40x28x+15\frac{x^{2}-13 x+40}{x^{2}-8 x+15}.

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Problem 18279

Convert the repeating decimal 0.510.\overline{51} into a fraction.

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Problem 18280

Solve for xx using the quadratic formula: 8x28x1=08 x^{2}-8 x-1=0. Provide solutions separated by commas. x=x=

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Problem 18281

Find ww in the equation 4w2+20w=254 w^{2}+20 w=-25. List all solutions or state "No solution."

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Problem 18282

Find the discriminant and the real solutions for the equation: 9x26x1=0-9 x^{2}-6 x-1=0.

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Problem 18283

Find a number to complete the expression as a perfect square: x2+6x+10x^{2}+6x+10.

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Problem 18284

Solve for ww: w29w+20=0w^{2}-9w+20=0. If multiple solutions, list them; if none, say "No solution."

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Problem 18285

Plot five points on the parabola y=34x2y=-\frac{3}{4} x^{2}: the vertex and two points on each side of it.

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Problem 18286

Select the factored form of the expression: 16x28x+1=16 x^{2}-8 x+1=

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Problem 18287

Choose the factored form for each expression: 16x28x+116 x^{2}-8 x+1, x2x30x^{2}-x-30, 9x2499 x^{2}-49, 3x2+17x63 x^{2}+17 x-6.

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Problem 18288

Determine if the function f(x)=2x2+12x20f(x)=-2 x^{2}+12 x-20 has a minimum or maximum, and find its value and location.

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Problem 18289

Evaluate the following functions at x=3x=3: f(x)=x3f(x)=x-3, g(x)=x23x+5g(x)=x^{2}-3x+5, h(x)=x3+x+33h(x)=\sqrt[3]{x^{3}+x+3}, p(x)=x2+1x+4p(x)=\frac{x^{2}+1}{x+4}, f(x)=x5f(x)=|x-5|. Also, for f(x)=x+8f(x)=x+8, find f(4)f(4), f(2)f(-2), f(x)f(-x), f(x+3)f(x+3), and f(x2+x+1)f\left(x^{2}+x+1\right).

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Problem 18290

Express v12v^{\frac{1}{2}} as a radical expression.

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Problem 18291

Simplify 9329^{\frac{3}{2}}.

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Problem 18292

Simplify the expression: z13z14z34\frac{z^{\frac{1}{3}}}{z^{\frac{1}{4}} z^{-\frac{3}{4}}} using only positive exponents.

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Problem 18293

Rewrite t34\sqrt[4]{t^{3}} as an exponential expression.

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Problem 18294

Simplify the expression: z14z13z12\frac{z^{-\frac{1}{4}}}{z^{\frac{1}{3}} z^{\frac{1}{2}}} using only positive exponents.

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Problem 18295

Simplify and write without exponents:
(181)34= \left(\frac{1}{81}\right)^{\frac{3}{4}}=\square and 3235= 32^{-\frac{3}{5}}=\square

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Problem 18296

Simplify the expression y12y17y32y^{-\frac{1}{2}} y^{-\frac{1}{7}} y^{\frac{3}{2}} using only positive exponents.

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Problem 18297

Simplify the expression: b12b13b14\frac{b^{-\frac{1}{2}} b^{\frac{1}{3}}}{b^{\frac{1}{4}}} using only positive exponents.

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Problem 18298

Simplify the expression (c2a45)15\left(c^{2} \cdot a^{-\frac{4}{5}}\right)^{\frac{1}{5}} without negative exponents.

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Problem 18299

Simplify the expression (z3y54)15\left(z^{-3} \cdot y^{\frac{5}{4}}\right)^{\frac{1}{5}} without negative exponents.

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Problem 18300

Simplify: 580+20-5 \sqrt{80} + \sqrt{20}.

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