Algebra Examples

$\frac{{(- 4)}^{2} m^{4} n^{- 7}}{{(- 2)}^{- 2} q^{5} r^{- 3}}$

Step 1

Simplify.

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Step 1.1

Move $n^{- 7}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{{(- 4)}^{2} m^{4}}{{(- 2)}^{- 2} q^{5} r^{- 3} n^{7}}$

Step 1.2

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

$\frac{{(- 4)}^{2} m^{4} {(- 2)}^{2}}{q^{5} r^{- 3} n^{7}}$

Step 1.3

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

$\frac{{(- 4)}^{2} m^{4} {(- 2)}^{2} r^{3}}{q^{5} n^{7}}$

Step 2

Simplify the numerator.

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Step 2.1

Raise $- 4$ to the power of $2$ .

$\frac{16 m^{4} {(- 2)}^{2} r^{3}}{q^{5} n^{7}}$

Step 2.2

Raise $- 2$ to the power of $2$ .

$\frac{16 m^{4} \cdot 4 r^{3}}{q^{5} n^{7}}$

Step 2.3

Multiply $4$ by $16$ .

$\frac{64 m^{4} r^{3}}{q^{5} n^{7}}$