Algebra Examples

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

Step 1

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

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Step 1.1

Multiply $3$ by $5$ .

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

Step 1.2

Combine using the product rule for radicals.

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

Step 1.3

Multiply $2$ by $16$ .

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

Step 1.4

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

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

Step 1.5

Add $3$ and $2$ .

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

Step 1.6

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

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Step 1.6.1

Move $y^{4}$ .

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

Step 1.6.2

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

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Step 1.6.2.1

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

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

Step 1.6.2.2

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

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

Step 1.6.3

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 $15$ .

$30 x y$