Simplify fifth root of 27x^2* fifth root of 9x^3

$\sqrt[5]{27 x^{2}} \cdot \sqrt[5]{9 x^{3}}$

Step 1

Multiply $\sqrt[5]{27 x^{2}} \sqrt[5]{9 x^{3}}$ .

Combine using the product rule for radicals.

$\sqrt[5]{27 x^{2} (9 x^{3})}$

Multiply $9$ by $27$ .

$\sqrt[5]{243 x^{2} x^{3}}$

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$\sqrt[5]{243 (x^{3} x^{2})}$

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

$\sqrt[5]{243 x^{3 + 2}}$

Add $3$ and $2$ .

$\sqrt[5]{243 x^{5}}$

Step 2

Rewrite $243 x^{5}$ as ${(3 x)}^{5}$ .

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

Step 3

Pull terms out from under the radical, assuming real numbers.

$3 x$