Algebra Examples

${(- 3 x^{5} y^{\frac{1}{3}})}^{3}$

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 $- 3 x^{5} y^{\frac{1}{3}}$ .

${(- 3 x^{5})}^{3} {(y^{\frac{1}{3}})}^{3}$

Step 1.2

Apply the product rule to $- 3 x^{5}$ .

${(- 3)}^{3} {(x^{5})}^{3} {(y^{\frac{1}{3}})}^{3}$

Step 2

Raise $- 3$ to the power of $3$ .

$- 27 {(x^{5})}^{3} {(y^{\frac{1}{3}})}^{3}$

Step 3

Multiply the exponents in ${(x^{5})}^{3}$ .

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Step 3.1

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

$- 27 x^{5 \cdot 3} {(y^{\frac{1}{3}})}^{3}$

Step 3.2

Multiply $5$ by $3$ .

$- 27 x^{15} {(y^{\frac{1}{3}})}^{3}$

Step 4

Multiply the exponents in ${(y^{\frac{1}{3}})}^{3}$ .

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Step 4.1

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

$- 27 x^{15} y^{\frac{1}{3} \cdot 3}$

Step 4.2

Cancel the common factor of $3$ .

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Step 4.2.1

Cancel the common factor.

$- 27 x^{15} y^{\frac{1}{3} \cdot 3}$

Step 4.2.2

Rewrite the expression.

$- 27 x^{15} y^{1}$

Step 5

Simplify.

$- 27 x^{15} y$