Algebra Examples

$\sqrt[5]{64 x^{4} y^{3}} \cdot \sqrt[5]{16 x y^{2}}$

Step 1

Rewrite $64 x^{4} y^{3}$ as $2^{5} \cdot (2 x^{4} y^{3})$ .

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Step 1.1

Factor $32$ out of $64$ .

$\sqrt[5]{32 (2) x^{4} y^{3}} \cdot \sqrt[5]{16 x y^{2}}$

Step 1.2

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

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

Step 1.3

Add parentheses.

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

Step 1.4

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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Step 3.1

Combine using the product rule for radicals.

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

Step 3.2

Multiply $2$ by $16$ .

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

Step 3.3

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

$2 \sqrt[5]{32 (x^{4} x^{1}) y^{2} y^{3}}$

Step 3.4

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

$2 \sqrt[5]{32 x^{4 + 1} y^{2} y^{3}}$

Step 3.5

Add $4$ and $1$ .

$2 \sqrt[5]{32 x^{5} y^{2} y^{3}}$

Step 3.6

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

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Step 3.6.1

Move $y^{3}$ .

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

Step 3.6.2

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

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

Step 3.6.3

Add $3$ and $2$ .

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

Step 4

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

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

Step 5

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

$2 (2 x y)$

Step 6

Multiply $2$ by $2$ .

$4 x y$