# How do you solve 1/32^(2x)=64?

Apr 25, 2016

$x = - \frac{3}{5}$

#### Explanation:

Using properties of exponents we are going to rewrite everything in terms of base $2$.

$\frac{1}{{32}^{2}} ^ x = 64$

$\frac{1}{{\left({2}^{5}\right)}^{2}} ^ x = 64$

$\frac{1}{2} ^ \left(10 x\right) = {2}^{6}$

${2}^{- 10 x} = {2}^{6}$

Since we are now in the same base we can do the following

$- 10 x = 6$

$x = \frac{6}{-} 10 = - \frac{3}{5}$