Write with Rational (Fractional) Exponents ( fourth root of x)^5

${(\sqrt[4]{x})}^{5}$

Step 1

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

${(x^{\frac{1}{4}})}^{5}$

Step 2

Multiply the exponents in ${(x^{\frac{1}{4}})}^{5}$ .

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

$x^{\frac{1}{4} \cdot 5}$

Combine $\frac{1}{4}$ and $5$ .

$x^{\frac{5}{4}}$