Question

Evaluate the expression.

${\mathbf{64}}^{2/3}$

Short answer

Answer is 16.

Step-by-step solution

Step 1. Understanding the concept of powers in fraction.

Fraction powers can be written as,

${\text{x}}^{\text{a/b}}\text{=}\sqrt[\text{b}]{{\text{x}}^{\text{a}}}$

Step 2. Re write the expression after solving fraction powers.

${\text{64}}^{\text{2/3}}\text{=}\sqrt[\text{3}]{{\left(\text{64}\right)}^{\text{2}}}$

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

$\begin{array}{c}\sqrt[\text{3}]{{\left(\text{64}\right)}^{\text{2}}}\text{=}\sqrt[\text{3}]{\text{64×64}}\\ \text{=}\sqrt[\text{3}]{\text{8×8×8×8}}\\ \text{=2×2×2×2}\\ \text{=16}\end{array}$