Question

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

Answer 1

Expression:

`((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:

`=((8^4)^2\cdot(5^3)^2)/((8^5)^2)`
`=(8^(4\cdot2)\cdot5^(3\cdot2))/(8^(5\cdot2))`
`=(8^8\cdot5^6)/(8^(10))`

Now we will use the Quotient rule:

`(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:

`=(8^8)/(8^(10))\cdot5^6`
`=8^(8-10)\cdot5^6`
`=8^(-2)\cdot5^6`

Answer:

`=8^(-2)\cdot5^6`