# How do you simplify 4^-sqrt7?

Oct 4, 2017

See a solution process below:

#### Explanation:

We can eliminate the negative exponent using this rule of exponents:

${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$

${4}^{\textcolor{red}{- \sqrt{7}}} \implies \frac{1}{4} ^ \textcolor{red}{- - \sqrt{7}} \implies \frac{1}{4} ^ \sqrt{7}$

If you need the actual number it is: 0.0255 rounded to the nearest thousandth.