Algebra Examples

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

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Multiply $- 2 x \frac{1}{y^{3}}$ .

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Step 2.1

Combine $- 2$ and $\frac{1}{y^{3}}$ .

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

Step 2.2

Combine $x$ and $\frac{- 2}{y^{3}}$ .

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

Step 3

Move $- 2$ to the left of $x$ .

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

Step 4

Move the negative in front of the fraction.

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

Step 5

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

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

Step 6

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

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Step 6.1

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

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

Step 6.2

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

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

Step 6.3

Apply the product rule to $2 x$ .

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

Step 7

Raise $- 1$ to the power of $2$ .

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

Step 8

Multiply $\frac{{(y^{3})}^{2}}{2^{2} x^{2}}$ by $1$ .

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

Step 9

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

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Step 9.1

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

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

Step 9.2

Multiply $3$ by $2$ .

$\frac{y^{6}}{2^{2} x^{2}}$

Step 10

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

$\frac{y^{6}}{4 x^{2}}$