Question

Rewrite each expression of two powers or a quotient of two powers

Answer 1

Expression:

$(\frac{8^4\cdot5^3}{8^5})^2$

To solve this expression first we have to use the Power rule:

$(a^x)^y=a^{x\cdot y}$

We can use this to simplify our expression as follows:

$=\frac{(8^4)^2\cdot(5^3)^2}{(8^5)^2}$$=\frac{8^{4\cdot2}\cdot5^{3\cdot2}}{8^{5\cdot2}}$$=\frac{8^8\cdot5^6}{8^{10}}$

Now we will use the Quotient rule:

$\frac{a^x}{a^y}=a^{x-y}$

To do that, we have to have the same number a, we cannot do this in the division of 5^6/8^10, but we can use it in 8^8/8^10:

$=\frac{8^8}{8^{10}}\cdot5^6$$=8^{8-10}\cdot5^6$$=8^{-2}\cdot5^6$

Answer:

$=8^{-2}\cdot5^6$