# How do you solve 25^ { 1- 3n } = 625^ { - n - 1}?

Sep 22, 2017

$n = 3$

#### Explanation:

Rewrite the expression by finding the same base on both sides

${25}^{1 - 3 n} = {625}^{- n - 1}$

$\Rightarrow {5}^{2 \left(1 - 3 n\right)} = {5}^{4 \left(- n - 1\right)}$

$\Rightarrow {5}^{2 - 6 n} = {5}^{- 4 n - 4}$

Equate the powers to solve for $n$

$2 - 6 n = - 4 n - 4$

$2 n = 6$

$n = 3$