Algebra Examples

${(64 x^{3} y)}^{\frac{2}{3}}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

Apply the product rule to $64 x^{3} y$ .

${(64 x^{3})}^{\frac{2}{3}} y^{\frac{2}{3}}$

Step 1.2

Apply the product rule to $64 x^{3}$ .

$64^{\frac{2}{3}} {(x^{3})}^{\frac{2}{3}} y^{\frac{2}{3}}$

Step 2

Simplify the expression.

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Step 2.1

Rewrite $64$ as $4^{3}$ .

${(4^{3})}^{\frac{2}{3}} {(x^{3})}^{\frac{2}{3}} y^{\frac{2}{3}}$

Step 2.2

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

$4^{3 (\frac{2}{3})} {(x^{3})}^{\frac{2}{3}} y^{\frac{2}{3}}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

$4^{3 (\frac{2}{3})} {(x^{3})}^{\frac{2}{3}} y^{\frac{2}{3}}$

Step 3.2

Rewrite the expression.

$4^{2} {(x^{3})}^{\frac{2}{3}} y^{\frac{2}{3}}$

Step 4

Simplify the expression.

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Step 4.1

Raise $4$ to the power of $2$ .

$16 {(x^{3})}^{\frac{2}{3}} y^{\frac{2}{3}}$

Step 4.2

Multiply the exponents in ${(x^{3})}^{\frac{2}{3}}$ .

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Step 4.2.1

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

$16 x^{3 (\frac{2}{3})} y^{\frac{2}{3}}$

Step 4.2.2

Cancel the common factor of $3$ .

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Step 4.2.2.1

Cancel the common factor.

$16 x^{3 (\frac{2}{3})} y^{\frac{2}{3}}$

Step 4.2.2.2

Rewrite the expression.

$16 x^{2} y^{\frac{2}{3}}$