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

${(\sqrt[5]{x^{7}})}^{3}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{x^{7}}$ as $x^{\frac{7}{5}}$ .

${(x^{\frac{7}{5}})}^{3}$

Step 2

Multiply the exponents in ${(x^{\frac{7}{5}})}^{3}$ .

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

$x^{\frac{7}{5} \cdot 3}$

Multiply $\frac{7}{5} \cdot 3$ .

Combine $\frac{7}{5}$ and $3$ .

$x^{\frac{7 \cdot 3}{5}}$

Multiply $7$ by $3$ .

$x^{\frac{21}{5}}$