Question

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

Answer 1

`81/x^4`

Explanation:

Given: `(x/3)^-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:

`(x/3)^-4 = x^-4/3^-4 = 3^4/x^4 = 81/x^4`

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

`(x/3)^-4 = (3/x)^4 = 3^4/x^4 = 81/x^4`