Algebra Examples

$(\frac{p^{2}}{q^{3}}) {(\frac{p}{q})}^{- 2}$

Step 1

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

$\frac{p^{2}}{q^{3}} {(\frac{q}{p})}^{2}$

Step 2

Apply the product rule to $\frac{q}{p}$ .

$\frac{p^{2}}{q^{3}} \cdot \frac{q^{2}}{p^{2}}$

Step 3

Combine.

$\frac{p^{2} q^{2}}{q^{3} p^{2}}$

Step 4

Cancel the common factor of $p^{2}$ .

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Step 4.1

Cancel the common factor.

$\frac{p^{2} q^{2}}{q^{3} p^{2}}$

Step 4.2

Rewrite the expression.

$\frac{q^{2}}{q^{3}}$

Step 5

Cancel the common factor of $q^{2}$ and $q^{3}$ .

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Step 5.1

Multiply by $1$ .

$\frac{q^{2} \cdot 1}{q^{3}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $q^{2}$ out of $q^{3}$ .

$\frac{q^{2} \cdot 1}{q^{2} q}$

Step 5.2.2

Cancel the common factor.

$\frac{q^{2} \cdot 1}{q^{2} q}$

Step 5.2.3

Rewrite the expression.

$\frac{1}{q}$