Write with Rational (Fractional) Exponents ( square root of 11)^5

${(\sqrt{11})}^{5}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{11}$ as $11^{\frac{1}{2}}$ .

${(11^{\frac{1}{2}})}^{5}$

Multiply the exponents in ${(11^{\frac{1}{2}})}^{5}$ .

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

$11^{\frac{1}{2} \cdot 5}$

Combine $\frac{1}{2}$ and $5$ .

$11^{\frac{5}{2}}$