Algebra Examples

${(- \frac{3 x^{4}}{2 y^{5}})}^{- 3}$

Step 1

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

${(- \frac{2 y^{5}}{3 x^{4}})}^{3}$

Step 2

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

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Step 2.1

Apply the product rule to $- \frac{2 y^{5}}{3 x^{4}}$ .

${(- 1)}^{3} {(\frac{2 y^{5}}{3 x^{4}})}^{3}$

Step 2.2

Apply the product rule to $\frac{2 y^{5}}{3 x^{4}}$ .

${(- 1)}^{3} \frac{{(2 y^{5})}^{3}}{{(3 x^{4})}^{3}}$

Step 2.3

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

${(- 1)}^{3} \frac{2^{3} {(y^{5})}^{3}}{{(3 x^{4})}^{3}}$

Step 2.4

Apply the product rule to $3 x^{4}$ .

${(- 1)}^{3} \frac{2^{3} {(y^{5})}^{3}}{3^{3} {(x^{4})}^{3}}$

Step 3

Raise $- 1$ to the power of $3$ .

$- \frac{2^{3} {(y^{5})}^{3}}{3^{3} {(x^{4})}^{3}}$

Step 4

Simplify the numerator.

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Step 4.1

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

$- \frac{8 {(y^{5})}^{3}}{3^{3} {(x^{4})}^{3}}$

Step 4.2

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

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Step 4.2.1

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

$- \frac{8 y^{5 \cdot 3}}{3^{3} {(x^{4})}^{3}}$

Step 4.2.2

Multiply $5$ by $3$ .

$- \frac{8 y^{15}}{3^{3} {(x^{4})}^{3}}$

Step 5

Simplify the denominator.

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Step 5.1

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

$- \frac{8 y^{15}}{27 {(x^{4})}^{3}}$

Step 5.2

Multiply the exponents in ${(x^{4})}^{3}$ .

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Step 5.2.1

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

$- \frac{8 y^{15}}{27 x^{4 \cdot 3}}$

Step 5.2.2

Multiply $4$ by $3$ .

$- \frac{8 y^{15}}{27 x^{12}}$