Write with Rational (Fractional) Exponents ( fourth root of 110)^7

${(\sqrt[4]{110})}^{7}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{110}$ as $110^{\frac{1}{4}}$ .

${(110^{\frac{1}{4}})}^{7}$

Step 2

Multiply the exponents in ${(110^{\frac{1}{4}})}^{7}$ .

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

$110^{\frac{1}{4} \cdot 7}$

Combine $\frac{1}{4}$ and $7$ .

$110^{\frac{7}{4}}$