Write the Fraction in Simplest Form ( square root of 7)^3

${(\sqrt{7})}^{3}$

Step 1

Rewrite ${\sqrt{7}}^{3}$ as ${(7^{3})}^{\frac{1}{2}}$ .

$\sqrt{7^{3}}$

Step 2

Raise $7$ to the power of $3$ .

$\sqrt{343}$

Step 3

Rewrite $343$ as $7^{2} \cdot 7$ .

Factor $49$ out of $343$ .

$\sqrt{49 (7)}$

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2} \cdot 7}$

Step 4

Pull terms out from under the radical.

$7 \sqrt{7}$