Write with Rational (Fractional) Exponents ( square root of 7)^3

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

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

${(7^{\frac{1}{2}})}^{3}$

Step 2

Multiply the exponents in ${(7^{\frac{1}{2}})}^{3}$ .

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

$7^{\frac{1}{2} \cdot 3}$

Combine $\frac{1}{2}$ and $3$ .

$7^{\frac{3}{2}}$