Algebra Examples

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

Step 1

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

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

Step 2

Multiply $y^{5}$ by $y^{2}$ by adding the exponents.

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Step 2.1

Move $y^{2}$ .

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

Step 2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.3

Add $2$ and $5$ .

${(\frac{x^{4}}{x^{- 3} y^{7}})}^{- 1}$

Step 3

Move $x^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{x^{4} x^{3}}{y^{7}})}^{- 1}$

Step 4

Multiply $x^{4}$ by $x^{3}$ by adding the exponents.

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Step 4.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{x^{4 + 3}}{y^{7}})}^{- 1}$

Step 4.2

Add $4$ and $3$ .

${(\frac{x^{7}}{y^{7}})}^{- 1}$

Step 5

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

$\frac{y^{7}}{x^{7}}$