Simplify 5 fifth root of 2x^3y^4*3 fifth root of 16x^2y

$5 \sqrt[5]{2 x^{3} y^{4}} \cdot 3 \sqrt[5]{16 x^{2} y}$

Step 1

Multiply $5 \sqrt[5]{2 x^{3} y^{4}} (3 \sqrt[5]{16 x^{2} y})$ .

Multiply $3$ by $5$ .

$15 \sqrt[5]{2 x^{3} y^{4}} \sqrt[5]{16 x^{2} y}$

Combine using the product rule for radicals.

$15 \sqrt[5]{16 x^{2} y (2 x^{3} y^{4})}$

Multiply $2$ by $16$ .

$15 \sqrt[5]{32 x^{2} y (x^{3} y^{4})}$

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

$15 \sqrt[5]{32 x^{3 + 2} y \cdot y^{4}}$

Add $3$ and $2$ .

$15 \sqrt[5]{32 x^{5} y \cdot y^{4}}$

Multiply $y$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

$15 \sqrt[5]{32 x^{5} (y^{4} y)}$

Multiply $y^{4}$ by $y$ .

Raise $y$ to the power of $1$ .

$15 \sqrt[5]{32 x^{5} (y^{4} y^{1})}$

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

$15 \sqrt[5]{32 x^{5} y^{4 + 1}}$

Add $4$ and $1$ .

$15 \sqrt[5]{32 x^{5} y^{5}}$

Step 2

Rewrite $32 x^{5} y^{5}$ as ${(2 x y)}^{5}$ .

$15 \sqrt[5]{{(2 x y)}^{5}}$

Step 3

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

$15 (2 x y)$

Step 4

Multiply $2$ by $15$ .

$30 x y$