Algebra Examples

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

Step 1

Cancel the common factor of $2$ and $4$ .

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Step 1.1

Factor $2$ out of $2 x^{2}$ .

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $4 y^{3}$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 3

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

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Step 3.1

Apply the product rule to $\frac{2 y^{3}}{x^{2}}$ .

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

Step 3.2

Apply the product rule to $2 y^{3}$ .

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

Step 4

Simplify the numerator.

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Step 4.1

Raise $2$ to the power of $3$ .

$\frac{8 {(y^{3})}^{3}}{{(x^{2})}^{3}}$

Step 4.2

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

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Step 4.2.1

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

$\frac{8 y^{3 \cdot 3}}{{(x^{2})}^{3}}$

Step 4.2.2

Multiply $3$ by $3$ .

$\frac{8 y^{9}}{{(x^{2})}^{3}}$

Step 5

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

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Step 5.1

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

$\frac{8 y^{9}}{x^{2 \cdot 3}}$

Step 5.2

Multiply $2$ by $3$ .

$\frac{8 y^{9}}{x^{6}}$