Question Simplify the expression $\frac{8^{6} \cdot 8^{2}}{8^{5}}$ and write the answer as a power.

Studdy Solution

STEP 1

Assumptions
1. We are given the expression $\frac{8^{6} \cdot 8^{2}}{8^{5}}$ .
2. We will use the properties of exponents to simplify the expression.

STEP 2

First, we apply the product of powers property, which states that when multiplying two powers with the same base, we can add the exponents.
$a^m \cdot a^n = a^{m+n}$

STEP 3

Apply the product of powers property to the numerator of the given expression.
$8^{6} \cdot 8^{2} = 8^{6+2}$

STEP 4

Calculate the sum of the exponents in the numerator.
$8^{6+2} = 8^{8}$

STEP 5

Now we have the simplified numerator, we rewrite the original expression with this new numerator.
$\frac{8^{8}}{8^{5}}$

STEP 6

Next, we apply the quotient of powers property, which states that when dividing two powers with the same base, we can subtract the exponents.
$\frac{a^m}{a^n} = a^{m-n}$

STEP 7

Apply the quotient of powers property to the expression.
$\frac{8^{8}}{8^{5}} = 8^{8-5}$

STEP 8

Calculate the difference of the exponents.
$8^{8-5} = 8^{3}$
The simplified expression is $8^{3}$ .

Was this helpful?

Question Simplify the expression $\frac{8^{6} \cdot 8^{2}}{8^{5}}$ and write the answer as a power.

Studdy Solution

STEP 1

Assumptions
1. We are given the expression $\frac{8^{6} \cdot 8^{2}}{8^{5}}$ .
2. We will use the properties of exponents to simplify the expression.

STEP 2

First, we apply the product of powers property, which states that when multiplying two powers with the same base, we can add the exponents.
$a^m \cdot a^n = a^{m+n}$

STEP 3

Apply the product of powers property to the numerator of the given expression.
$8^{6} \cdot 8^{2} = 8^{6+2}$

STEP 4

Calculate the sum of the exponents in the numerator.
$8^{6+2} = 8^{8}$

STEP 5

Now we have the simplified numerator, we rewrite the original expression with this new numerator.
$\frac{8^{8}}{8^{5}}$

STEP 6

Next, we apply the quotient of powers property, which states that when dividing two powers with the same base, we can subtract the exponents.
$\frac{a^m}{a^n} = a^{m-n}$

STEP 7

Apply the quotient of powers property to the expression.
$\frac{8^{8}}{8^{5}} = 8^{8-5}$

STEP 8

Calculate the difference of the exponents.
$8^{8-5} = 8^{3}$
The simplified expression is $8^{3}$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question Simplify the expression 86⋅8285\frac{8^{6} \cdot 8^{2}}{8^{5}}8586⋅82​ and write the answer as a power.

Studdy Solution

STEP 1

Assumptions1. We are given the expression 86⋅8285\frac{8^{6} \cdot 8^{2}}{8^{5}}8586⋅82​.2. We will use the properties of exponents to simplify the expression.

STEP 2

First, we apply the product of powers property, which states that when multiplying two powers with the same base, we can add the exponents.am⋅an=am+na^m \cdot a^n = a^{m+n}am⋅an=am+n

STEP 3

Apply the product of powers property to the numerator of the given expression.86⋅82=86+28^{6} \cdot 8^{2} = 8^{6+2}86⋅82=86+2

STEP 4

Calculate the sum of the exponents in the numerator.86+2=888^{6+2} = 8^{8}86+2=88

STEP 5

Now we have the simplified numerator, we rewrite the original expression with this new numerator.8885\frac{8^{8}}{8^{5}}8588​

STEP 6

Next, we apply the quotient of powers property, which states that when dividing two powers with the same base, we can subtract the exponents.aman=am−n\frac{a^m}{a^n} = a^{m-n}anam​=am−n

STEP 7

Apply the quotient of powers property to the expression.8885=88−5\frac{8^{8}}{8^{5}} = 8^{8-5}8588​=88−5

STEP 8

Calculate the difference of the exponents.88−5=838^{8-5} = 8^{3}88−5=83The simplified expression is 838^{3}83.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question Simplify the expression $\frac{8^{6} \cdot 8^{2}}{8^{5}}$ and write the answer as a power.

Assumptions
1. We are given the expression $\frac{8^{6} \cdot 8^{2}}{8^{5}}$ .
2. We will use the properties of exponents to simplify the expression.

First, we apply the product of powers property, which states that when multiplying two powers with the same base, we can add the exponents.
$a^m \cdot a^n = a^{m+n}$

Apply the product of powers property to the numerator of the given expression.
$8^{6} \cdot 8^{2} = 8^{6+2}$

Calculate the sum of the exponents in the numerator.
$8^{6+2} = 8^{8}$

Now we have the simplified numerator, we rewrite the original expression with this new numerator.
$\frac{8^{8}}{8^{5}}$

Next, we apply the quotient of powers property, which states that when dividing two powers with the same base, we can subtract the exponents.
$\frac{a^m}{a^n} = a^{m-n}$

Apply the quotient of powers property to the expression.
$\frac{8^{8}}{8^{5}} = 8^{8-5}$

Calculate the difference of the exponents.
$8^{8-5} = 8^{3}$
The simplified expression is $8^{3}$ .