Write with Rational (Fractional) Exponents square root of square root of 625

$\sqrt{\sqrt{625}}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{625}$ as $625^{\frac{1}{2}}$ .

$\sqrt{625^{\frac{1}{2}}}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{625^{\frac{1}{2}}}$ as $625^{\frac{\frac{1}{2}}{2}}$ .

$625^{\frac{\frac{1}{2}}{2}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$625^{\frac{1}{2} \cdot \frac{1}{2}}$

Step 4

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

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

$625^{\frac{1}{2 \cdot 2}}$

Multiply $2$ by $2$ .

$625^{\frac{1}{4}}$