Pre-Algebra Examples

${(\sqrt[7]{5 x^{2} y})}^{4}$

Step 1

Rewrite ${\sqrt[7]{5 x^{2} y}}^{4}$ as $\sqrt[7]{{(5 x^{2} y)}^{4}}$ .

$\sqrt[7]{{(5 x^{2} y)}^{4}}$

Step 2

Apply the product rule to $5 x^{2} y$ .

$\sqrt[7]{{(5 x^{2})}^{4} y^{4}}$

Step 3

Apply the product rule to $5 x^{2}$ .

$\sqrt[7]{5^{4} {(x^{2})}^{4} y^{4}}$

Step 4

Raise $5$ to the power of $4$ .

$\sqrt[7]{625 {(x^{2})}^{4} y^{4}}$

Step 5

Multiply the exponents in ${(x^{2})}^{4}$ .

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Step 5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\sqrt[7]{625 x^{2 \cdot 4} y^{4}}$

Step 5.2

Multiply $2$ by $4$ .

$\sqrt[7]{625 x^{8} y^{4}}$

Step 6

Rewrite $625 x^{8} y^{4}$ as $x^{7} \cdot (625 x y^{4})$ .

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Step 6.1

Factor out $x^{7}$ .

$\sqrt[7]{625 (x^{7} x) y^{4}}$

Step 6.2

Reorder $625$ and $x^{7}$ .

$\sqrt[7]{x^{7} \cdot 625 x y^{4}}$

Step 6.3

Add parentheses.

$\sqrt[7]{x^{7} \cdot 625 (x y^{4})}$

Step 6.4

Add parentheses.

$\sqrt[7]{x^{7} \cdot (625 x y^{4})}$

Step 7

Pull terms out from under the radical.

$x \sqrt[7]{625 x y^{4}}$