Algebra Examples

$\frac{3 q^{2}}{- 2 {(p^{3} q^{- 5})}^{- 1}}$

Step 1

Move ${(p^{3} q^{- 5})}^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{3 q^{2} (p^{3} q^{- 5})}{- 2}$

Step 2

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

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Step 2.1

Move $q^{- 5}$ .

$\frac{3 (q^{- 5} q^{2}) p^{3}}{- 2}$

Step 2.2

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

$\frac{3 q^{- 5 + 2} p^{3}}{- 2}$

Step 2.3

Add $- 5$ and $2$ .

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

Step 3

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

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

Step 4

Move the negative in front of the fraction.

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