Write with Rational (Fractional) Exponents ( eighth root of 9)^5

${(\sqrt[8]{9})}^{5}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[8]{9}$ as $9^{\frac{1}{8}}$ .

${(9^{\frac{1}{8}})}^{5}$

Step 2

Multiply the exponents in ${(9^{\frac{1}{8}})}^{5}$ .

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

$9^{\frac{1}{8} \cdot 5}$

Combine $\frac{1}{8}$ and $5$ .

$9^{\frac{5}{8}}$