Simplify ( sixth root of x)^3

${(\sqrt[6]{x})}^{3}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[6]{x}$ as $x^{\frac{1}{6}}$ .

${(x^{\frac{1}{6}})}^{3}$

Step 2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{6} \cdot 3}$

Step 3

Combine $\frac{1}{6}$ and $3$ .

$x^{\frac{3}{6}}$

Step 4

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$x^{\frac{3 (1)}{6}}$

Cancel the common factors.

Factor $3$ out of $6$ .

$x^{\frac{3 \cdot 1}{3 \cdot 2}}$

Cancel the common factor.

$x^{\frac{3 \cdot 1}{3 \cdot 2}}$

Rewrite the expression.

$x^{\frac{1}{2}}$

Step 5

Rewrite $x^{\frac{1}{2}}$ as $\sqrt{x}$ .

$\sqrt{x}$