Simplify ( sixth root of x^5)^7

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

Step 1

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

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

Step 2

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

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

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

Multiply $5$ by $7$ .

$\sqrt[6]{x^{35}}$

Step 3

Rewrite $x^{35}$ as ${(x^{5})}^{6} x^{5}$ .

Factor out $x^{30}$ .

$\sqrt[6]{x^{30} x^{5}}$

Rewrite $x^{30}$ as ${(x^{5})}^{6}$ .

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

Step 4

Pull terms out from under the radical.

$x^{5} \sqrt[6]{x^{5}}$