Question

Evaluate the expression.

${\mathbf{216}}^{-1/3}$

Short answer

Answer is $\frac{1}{6}$.

Step-by-step solution

Step 1. Understanding the concept of negative powers.

Negative power can be written as,

${\text{x}}^{\text{-1}}\text{=}\frac{\text{1}}{\text{x}}$

Step 2. Re write the expression after changing negative powers to fraction.

${216}^{-1/3}=\frac{1}{{216}^{1/3}}$

Step 3. Simplify the expression by solving the cube root.

$\begin{array}{c}\frac{\text{1}}{{\text{216}}^{\text{1/3}}}\text{=}\frac{\text{1}}{\sqrt[3]{6\times 6\times 6}}\\ \text{=}\frac{1}{6}\end{array}$