Algebra Examples

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

Step 1

Move $x^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Move $y^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 3

Multiply $y$ by $y$ .

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

Step 4

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

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

Step 5

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

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

Step 6

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

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Step 6.1

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

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

Step 6.2

Multiply $2$ by $3$ .

$\frac{x^{6}}{{(y^{2})}^{3}}$

Step 7

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

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Step 7.1

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

$\frac{x^{6}}{y^{2 \cdot 3}}$

Step 7.2

Multiply $2$ by $3$ .

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