Algebra Examples

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

Step 1

Move $x^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Cancel the common factor of $y$ and $y^{3}$ .

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Step 2.1

Raise $y$ to the power of $1$ .

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

Step 2.2

Factor $y$ out of $y^{1}$ .

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

Step 2.3

Cancel the common factors.

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Step 2.3.1

Factor $y$ out of $y^{3} x^{5}$ .

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

Step 2.3.2

Cancel the common factor.

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

Step 2.3.3

Rewrite the expression.

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

Step 3

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

$y^{2} x^{5}$