Algebra Examples

$\sqrt[5]{8 x^{3} y} \cdot \sqrt[5]{4 x^{4} y}$

Step 1

Multiply $\sqrt[5]{8 x^{3} y} \sqrt[5]{4 x^{4} y}$ .

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Step 1.1

Combine using the product rule for radicals.

$\sqrt[5]{8 x^{3} y (4 x^{4} y)}$

Step 1.2

Multiply $4$ by $8$ .

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

Step 1.3

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

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

Step 1.4

Add $4$ and $3$ .

$\sqrt[5]{32 x^{7} y \cdot y}$

Step 1.5

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

$\sqrt[5]{32 x^{7} (y^{1} y)}$

Step 1.6

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

$\sqrt[5]{32 x^{7} (y^{1} y^{1})}$

Step 1.7

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

$\sqrt[5]{32 x^{7} y^{1 + 1}}$

Step 1.8

Add $1$ and $1$ .

$\sqrt[5]{32 x^{7} y^{2}}$

Step 2

Rewrite $32 x^{7} y^{2}$ as ${(2 x)}^{5} (x^{2} y^{2})$ .

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Step 2.1

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

$\sqrt[5]{2^{5} x^{7} y^{2}}$

Step 2.2

Factor out $x^{5}$ .

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

Step 2.3

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

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

Step 2.4

Add parentheses.

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

Step 3

Pull terms out from under the radical.

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