Simplify ( fifth root of 28x^2)^3

${(\sqrt[5]{28 x^{2}})}^{3}$

Step 1

Rewrite ${\sqrt[5]{28 x^{2}}}^{3}$ as ${({(28 x^{2})}^{3})}^{\frac{1}{5}}$ .

$\sqrt[5]{{(28 x^{2})}^{3}}$

Step 2

Apply the product rule to $28 x^{2}$ .

$\sqrt[5]{28^{3} {(x^{2})}^{3}}$

Step 3

Raise $28$ to the power of $3$ .

$\sqrt[5]{21952 {(x^{2})}^{3}}$

Step 4

Multiply the exponents in ${(x^{2})}^{3}$ .

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

$\sqrt[5]{21952 x^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$\sqrt[5]{21952 x^{6}}$

Step 5

Rewrite $21952 x^{6}$ as ${(2 x)}^{5} \cdot (686 x)$ .

Factor $32$ out of $21952$ .

$\sqrt[5]{32 (686) x^{6}}$

Rewrite $32$ as $2^{5}$ .

$\sqrt[5]{2^{5} \cdot 686 x^{6}}$

Factor out $x^{5}$ .

$\sqrt[5]{2^{5} \cdot 686 (x^{5} x)}$

Move $686$ .

$\sqrt[5]{2^{5} x^{5} \cdot 686 x}$

Rewrite $2^{5} x^{5}$ as ${(2 x)}^{5}$ .

$\sqrt[5]{{(2 x)}^{5} \cdot 686 x}$

Add parentheses.

$\sqrt[5]{{(2 x)}^{5} \cdot (686 x)}$

Step 6

Pull terms out from under the radical.

$2 x \sqrt[5]{686 x}$