Question

Find the value of n 5^10 ÷ 5^8=(1/5)^n

Answer 1

`n=-2`

Explanation:

`(5^(10))/(5^8)=((1)/(5))^n`

Use the law of exponents.

`5^(10-8)=\left((1)/(5)\right)^n`

1/5 can be written with a base of 5.

`5^(10-8)=\left(5^(-1)\right)^n`

Cancel the base 5 on both sides.

`10-8=-1* \:n`

`2=-n`

Multiply both sides with -1.

`n=-2`

Answer 2

5^10 / 5^8 = 5^2 = 25 so the equation becomes 25 = (1/5) ^ n. This means that n = -2.