# Question #46e8f

Jan 29, 2018

$\frac{1}{2401}$

#### Explanation:

${\left(\frac{1}{4}\right)}^{2 x} = {\left(\frac{1}{{2}^{2}}\right)}^{2 x} = {\left({2}^{- 2}\right)}^{2 x}$

$= {2}^{- 4 x} = {\left({2}^{x}\right)}^{- 4}$

Since it's given that ${2}^{x} = 7$, we can substitute to get:

${\left({2}^{x}\right)}^{- 4} = {\left(7\right)}^{- 4} = \frac{1}{2401}$