Write in Exponential Form square root of cube root of 64

$\sqrt{\sqrt[3]{64}}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{64}$ as $64^{\frac{1}{3}}$ .

$\sqrt{64^{\frac{1}{3}}}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{64^{\frac{1}{3}}}$ as $64^{\frac{\frac{1}{3}}{2}}$ .

$64^{\frac{\frac{1}{3}}{2}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$64^{\frac{1}{3} \cdot \frac{1}{2}}$

Step 4

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

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

$64^{\frac{1}{3 \cdot 2}}$

Multiply $3$ by $2$ .

$64^{\frac{1}{6}}$