Basic Math Examples

$\frac{- 4 m^{5} n^{4}}{{(24 m n^{- 7})}^{- 2}}$

Step 1

Move ${(24 m n^{- 7})}^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$- 4 m^{5} n^{4} {(24 m n^{- 7})}^{2}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- 4 m^{5} n^{4} {(24 m \frac{1}{n^{7}})}^{2}$

Step 3

Multiply $24 m \frac{1}{n^{7}}$ .

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Step 3.1

Combine $24$ and $\frac{1}{n^{7}}$ .

$- 4 m^{5} n^{4} {(m \frac{24}{n^{7}})}^{2}$

Step 3.2

Combine $m$ and $\frac{24}{n^{7}}$ .

$- 4 m^{5} n^{4} {(\frac{m \cdot 24}{n^{7}})}^{2}$

Step 4

Move $24$ to the left of $m$ .

$- 4 m^{5} n^{4} {(\frac{24 \cdot m}{n^{7}})}^{2}$

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 5.1

Apply the product rule to $\frac{24 m}{n^{7}}$ .

$- 4 m^{5} n^{4} \frac{{(24 m)}^{2}}{{(n^{7})}^{2}}$

Step 5.2

Apply the product rule to $24 m$ .

$- 4 m^{5} n^{4} \frac{24^{2} m^{2}}{{(n^{7})}^{2}}$

Step 6

Simplify the expression.

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Step 6.1

Raise $24$ to the power of $2$ .

$- 4 m^{5} n^{4} \frac{576 m^{2}}{{(n^{7})}^{2}}$

Step 6.2

Multiply the exponents in ${(n^{7})}^{2}$ .

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Step 6.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 4 m^{5} n^{4} \frac{576 m^{2}}{n^{7 \cdot 2}}$

Step 6.2.2

Multiply $7$ by $2$ .

$- 4 m^{5} n^{4} \frac{576 m^{2}}{n^{14}}$

Step 7

Cancel the common factor of $n^{4}$ .

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Step 7.1

Factor $n^{4}$ out of $- 4 m^{5} n^{4}$ .

$n^{4} (- 4 m^{5}) \frac{576 m^{2}}{n^{14}}$

Step 7.2

Factor $n^{4}$ out of $n^{14}$ .

$n^{4} (- 4 m^{5}) \frac{576 m^{2}}{n^{4} n^{10}}$

Step 7.3

Cancel the common factor.

$n^{4} (- 4 m^{5}) \frac{576 m^{2}}{n^{4} n^{10}}$

Step 7.4

Rewrite the expression.

$- 4 m^{5} \frac{576 m^{2}}{n^{10}}$

Step 8

Combine $- 4$ and $\frac{576 m^{2}}{n^{10}}$ .

$m^{5} \frac{- 4 (576 m^{2})}{n^{10}}$

Step 9

Multiply $576$ by $- 4$ .

$m^{5} \frac{- 2304 m^{2}}{n^{10}}$

Step 10

Combine $m^{5}$ and $\frac{- 2304 m^{2}}{n^{10}}$ .

$\frac{m^{5} (- 2304 m^{2})}{n^{10}}$

Step 11

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

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Step 11.1

Move $m^{2}$ .

$\frac{m^{2} m^{5} \cdot - 2304}{n^{10}}$

Step 11.2

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

$\frac{m^{2 + 5} \cdot - 2304}{n^{10}}$

Step 11.3

Add $2$ and $5$ .

$\frac{m^{7} \cdot - 2304}{n^{10}}$

Step 12

Move $- 2304$ to the left of $m^{7}$ .

$\frac{- 2304 \cdot m^{7}}{n^{10}}$

Step 13

Move the negative in front of the fraction.

$- \frac{2304 m^{7}}{n^{10}}$