Pre-Algebra Examples

${(\sqrt[6]{5 x y^{5}})}^{7}$

Step 1

Rewrite ${\sqrt[6]{5 x y^{5}}}^{7}$ as $\sqrt[6]{{(5 x y^{5})}^{7}}$ .

$\sqrt[6]{{(5 x y^{5})}^{7}}$

Step 2

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

$\sqrt[6]{{(5 x)}^{7} {(y^{5})}^{7}}$

Step 3

Apply the product rule to $5 x$ .

$\sqrt[6]{5^{7} x^{7} {(y^{5})}^{7}}$

Step 4

Raise $5$ to the power of $7$ .

$\sqrt[6]{78125 x^{7} {(y^{5})}^{7}}$

Step 5

Multiply the exponents in ${(y^{5})}^{7}$ .

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Step 5.1

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

$\sqrt[6]{78125 x^{7} y^{5 \cdot 7}}$

Step 5.2

Multiply $5$ by $7$ .

$\sqrt[6]{78125 x^{7} y^{35}}$

Step 6

Rewrite $78125 x^{7} y^{35}$ as ${(5 x y^{5})}^{6} \cdot (5 x y^{5})$ .

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Step 6.1

Factor $15625$ out of $78125$ .

$\sqrt[6]{15625 (5) x^{7} y^{35}}$

Step 6.2

Rewrite $15625$ as $5^{6}$ .

$\sqrt[6]{5^{6} \cdot 5 x^{7} y^{35}}$

Step 6.3

Factor out $x^{6}$ .

$\sqrt[6]{5^{6} \cdot 5 (x^{6} x) y^{35}}$

Step 6.4

Factor out $y^{30}$ .

$\sqrt[6]{5^{6} \cdot 5 (x^{6} x) (y^{30} y^{5})}$

Step 6.5

Rewrite $y^{30}$ as ${(y^{5})}^{6}$ .

$\sqrt[6]{5^{6} \cdot 5 (x^{6} x) ({(y^{5})}^{6} y^{5})}$

Step 6.6

Move $x$ .

$\sqrt[6]{5^{6} \cdot 5 (x^{6}) {(y^{5})}^{6} x y^{5}}$

Step 6.7

Move $5$ .

$\sqrt[6]{5^{6} (x^{6}) {(y^{5})}^{6} \cdot 5 x y^{5}}$

Step 6.8

Rewrite $(5^{6} (x^{6})) {(y^{5})}^{6}$ as ${(5 x y^{5})}^{6}$ .

$\sqrt[6]{{(5 x y^{5})}^{6} \cdot 5 x y^{5}}$

Step 6.9

Add parentheses.

$\sqrt[6]{{(5 x y^{5})}^{6} \cdot 5 (x y^{5})}$

Step 6.10

Add parentheses.

$\sqrt[6]{{(5 x y^{5})}^{6} \cdot (5 x y^{5})}$

Step 7

Pull terms out from under the radical.

$5 x y^{5} \sqrt[6]{5 x y^{5}}$