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

Answer 1

#81/x^4#

Given: #(x/3)^-4#

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

One method is to assign the exponent to the denominator as well as the numerator, and then shift the exponents to the opposite side to make them positive:

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

Changing the exponent to positive and flipping the numerator and denominator is a second method of simplification:

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

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Answer 2

Kennedy Adams

To simplify (x/3)^-4, you can rewrite it as 3^4/x^4, which simplifies further to 81/x^4.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.