Algebra Examples

$\sqrt[3]{\sqrt{2 x}}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x}$ as ${(2 x)}^{\frac{1}{2}}$ .

$\sqrt[3]{{(2 x)}^{\frac{1}{2}}}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{{(2 x)}^{\frac{1}{2}}}$ as ${(2 x)}^{\frac{\frac{1}{2}}{3}}$ .

${(2 x)}^{\frac{\frac{1}{2}}{3}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

Multiply $\frac{1}{2} \cdot \frac{1}{3}$ .

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Step 4.1

Multiply $\frac{1}{2}$ by $\frac{1}{3}$ .

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

Step 4.2

Multiply $2$ by $3$ .

${(2 x)}^{\frac{1}{6}}$