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How do you simplify #(1/27)^(-2/3)#?

Answer 1

Eva Adamson

See a solution process below:

Using these rules for exponents we can rewrite the expression as:

#(1/27)^(color(red)(1/3) xx color(blue)(-2) =>#

#((1/27)^(color(red)(1/3)))^color(blue)(-2) =>#

#(1^color(red)(1/3)/27^color(red)(1/3))^color(blue)(-2) =>#

#(1/3)^color(blue)(-2) =>#

#1^color(blue)(-2)/3^color(blue)(-2) =>#

#1/3^color(blue)(-2) =>#

#3^color(blue)(- -2) =>#

#3^color(blue)(2) =>#

#9#

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Answer 2

Eva Adamson

To simplify (1/27)^(-2/3), you can first rewrite it as (27)^(-2/3). Then, applying the property of exponentiation, you raise the base 27 to the exponent -2/3. This results in the reciprocal of the cube root of 27 raised to the power of 2. Therefore, the simplified form is 1/(cube root of 27)^2. Simplifying further, the cube root of 27 is 3, so the final result is 1/9.

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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.