Simplify fifth root of 4x^2* fifth root of 4x^2

$\sqrt[5]{4 x^{2}} \cdot \sqrt[5]{4 x^{2}}$

Step 1

Multiply $\sqrt[5]{4 x^{2}} \sqrt[5]{4 x^{2}}$ .

Raise $\sqrt[5]{4 x^{2}}$ to the power of $1$ .

${\sqrt[5]{4 x^{2}}}^{1} \sqrt[5]{4 x^{2}}$

Raise $\sqrt[5]{4 x^{2}}$ to the power of $1$ .

${\sqrt[5]{4 x^{2}}}^{1} {\sqrt[5]{4 x^{2}}}^{1}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\sqrt[5]{4 x^{2}}}^{1 + 1}$

Add $1$ and $1$ .

${\sqrt[5]{4 x^{2}}}^{2}$

Step 2

Rewrite ${\sqrt[5]{4 x^{2}}}^{2}$ as $\sqrt[5]{{(4 x^{2})}^{2}}$ .

$\sqrt[5]{{(4 x^{2})}^{2}}$

Step 3

Apply the product rule to $4 x^{2}$ .

$\sqrt[5]{4^{2} {(x^{2})}^{2}}$

Step 4

Raise $4$ to the power of $2$ .

$\sqrt[5]{16 {(x^{2})}^{2}}$

Step 5

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

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

$\sqrt[5]{16 x^{2 \cdot 2}}$

Multiply $2$ by $2$ .

$\sqrt[5]{16 x^{4}}$