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

1 Answer
May 21, 2018

Answer:

#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#