Question

which expression is equivalent to $8x^{\frac{3}{8}}$? $64x^{3}$ $64\sqrt{x^{3}}$ $8\sqrt8{x^{3}}$ $\sqrt8{8x^{3}}$

Explanation:

Step1: Recall exponent-root rule

For $x^{\frac{m}{n}} = \sqrt[n]{x^m}$

Step2: Apply rule to $x^\frac{3}{8}$

$x^{\frac{3}{8}} = \sqrt[8]{x^3}$

Step3: Multiply by the constant term

$8x^{\frac{3}{8}} = 8\sqrt[8]{x^3}$

Answer:

$8\sqrt[8]{x^3}$ (the third option)