Write with Rational (Fractional) Exponents ( sixth root of x^5)^7

${(\sqrt[6]{x^{5}})}^{7}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[6]{x^{5}}$ as $x^{\frac{5}{6}}$ .

${(x^{\frac{5}{6}})}^{7}$

Step 2

Multiply the exponents in ${(x^{\frac{5}{6}})}^{7}$ .

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

$x^{\frac{5}{6} \cdot 7}$

Multiply $\frac{5}{6} \cdot 7$ .

Combine $\frac{5}{6}$ and $7$ .

$x^{\frac{5 \cdot 7}{6}}$

Multiply $5$ by $7$ .

$x^{\frac{35}{6}}$