# How do you simplify (x/3)^-4?

May 21, 2018

$\frac{81}{x} ^ 4$

#### Explanation:

Given: ${\left(\frac{x}{3}\right)}^{-} 4$

Exponent Rules: (x/y)^n = x^n/y^n; " "x^-n = 1/x^n; " "1/x^-n = x^n

One way is to distribute the exponent to both the numerator and denominator, then make the exponents positive by moving them to the opposite side:

${\left(\frac{x}{3}\right)}^{-} 4 = {x}^{-} \frac{4}{3} ^ - 4 = {3}^{4} / {x}^{4} = \frac{81}{x} ^ 4$

A second way to simplify is to flip the numerator and denominator and change the exponent to positive:

${\left(\frac{x}{3}\right)}^{-} 4 = {\left(\frac{3}{x}\right)}^{4} = {3}^{4} / {x}^{4} = \frac{81}{x} ^ 4$