Question

write the expression in radical form and then evaluate.
$27^{-1/3}$
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. $27^{-1/3}=\square$ (simplify your answer. type an integer or a fraction.)
b. the answer is not a real number.

Explanation:

Step1: Recall negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\). So, \(27^{-1/3}=\frac{1}{27^{1/3}}\).

Step2: Recall fractional exponent rule

The fractional exponent rule \(a^{m/n}=\sqrt[n]{a^{m}}\). For \(27^{1/3}\), this is \(\sqrt[3]{27^{1}}\) or \(\sqrt[3]{27}\).

Step3: Evaluate the cube root

We know that \(3\times3\times3 = 27\), so \(\sqrt[3]{27}=3\). Then \(\frac{1}{27^{1/3}}=\frac{1}{3}\).

Answer:

A. \(27^{-1/3}=\frac{1}{3}\)