Basic Math Examples

$\frac{{(- 4 m^{3})}^{2} {(n^{- 2})}^{2}}{{(2^{- 1})}^{2} m^{4} n^{- 8}}$

Step 1

Move $n^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(- 4 m^{3})}^{2} {(n^{- 2})}^{2} n^{8}}{{(2^{- 1})}^{2} m^{4}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $- 4 m^{3}$ .

$\frac{{(- 4)}^{2} {(m^{3})}^{2} {(n^{- 2})}^{2} n^{8}}{{(2^{- 1})}^{2} m^{4}}$

Step 2.2

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

$\frac{16 {(m^{3})}^{2} {(n^{- 2})}^{2} n^{8}}{{(2^{- 1})}^{2} m^{4}}$

Step 2.3

Multiply the exponents in ${(m^{3})}^{2}$ .

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Step 2.3.1

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

$\frac{16 m^{3 \cdot 2} {(n^{- 2})}^{2} n^{8}}{{(2^{- 1})}^{2} m^{4}}$

Step 2.3.2

Multiply $3$ by $2$ .

$\frac{16 m^{6} {(n^{- 2})}^{2} n^{8}}{{(2^{- 1})}^{2} m^{4}}$

Step 2.4

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

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Step 2.4.1

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

$\frac{16 m^{6} n^{- 2 \cdot 2} n^{8}}{{(2^{- 1})}^{2} m^{4}}$

Step 2.4.2

Multiply $- 2$ by $2$ .

$\frac{16 m^{6} n^{- 4} n^{8}}{{(2^{- 1})}^{2} m^{4}}$

Step 2.5

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

$\frac{16 m^{6} \frac{1}{n^{4}} n^{8}}{{(2^{- 1})}^{2} m^{4}}$

Step 2.6

Combine exponents.

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Step 2.6.1

Combine $16$ and $\frac{1}{n^{4}}$ .

$\frac{m^{6} \frac{16}{n^{4}} n^{8}}{{(2^{- 1})}^{2} m^{4}}$

Step 2.6.2

Combine $m^{6}$ and $\frac{16}{n^{4}}$ .

$\frac{\frac{m^{6} \cdot 16}{n^{4}} n^{8}}{{(2^{- 1})}^{2} m^{4}}$

Step 2.6.3

Combine $\frac{m^{6} \cdot 16}{n^{4}}$ and $n^{8}$ .

$\frac{\frac{m^{6} \cdot 16 n^{8}}{n^{4}}}{{(2^{- 1})}^{2} m^{4}}$

Step 2.7

Reduce the expression by cancelling the common factors.

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Step 2.7.1

Reduce the expression $\frac{m^{6} \cdot 16 n^{8}}{n^{4}}$ by cancelling the common factors.

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Step 2.7.1.1

Factor $n^{4}$ out of $m^{6} \cdot 16 n^{8}$ .

$\frac{\frac{n^{4} (m^{6} \cdot 16 n^{4})}{n^{4}}}{{(2^{- 1})}^{2} m^{4}}$

Step 2.7.1.2

Multiply by $1$ .

$\frac{\frac{n^{4} (m^{6} \cdot 16 n^{4})}{n^{4} \cdot 1}}{{(2^{- 1})}^{2} m^{4}}$

Step 2.7.1.3

Cancel the common factor.

$\frac{\frac{n^{4} (m^{6} \cdot 16 n^{4})}{n^{4} \cdot 1}}{{(2^{- 1})}^{2} m^{4}}$

Step 2.7.1.4

Rewrite the expression.

$\frac{\frac{m^{6} \cdot 16 n^{4}}{1}}{{(2^{- 1})}^{2} m^{4}}$

Step 2.7.2

Divide $m^{6} \cdot 16 n^{4}$ by $1$ .

$\frac{m^{6} \cdot 16 n^{4}}{{(2^{- 1})}^{2} m^{4}}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply the exponents in ${(2^{- 1})}^{2}$ .

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Step 3.1.1

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

$\frac{m^{6} \cdot 16 n^{4}}{2^{- 1 \cdot 2} m^{4}}$

Step 3.1.2

Multiply $- 1$ by $2$ .

$\frac{m^{6} \cdot 16 n^{4}}{2^{- 2} m^{4}}$

Step 3.2

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

$\frac{m^{6} \cdot 16 n^{4}}{\frac{1}{2^{2}} m^{4}}$

Step 3.3

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

$\frac{m^{6} \cdot 16 n^{4}}{\frac{1}{4} m^{4}}$

Step 4

Combine $\frac{1}{4}$ and $m^{4}$ .

$\frac{m^{6} \cdot 16 n^{4}}{\frac{m^{4}}{4}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$m^{6} \cdot 16 n^{4} \frac{4}{m^{4}}$

Step 6

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

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Step 6.1

Factor $m^{4}$ out of $m^{6} \cdot 16 n^{4}$ .

$m^{4} (m^{2} \cdot 16 n^{4}) \frac{4}{m^{4}}$

Step 6.2

Cancel the common factor.

$m^{4} (m^{2} \cdot 16 n^{4}) \frac{4}{m^{4}}$

Step 6.3

Rewrite the expression.

$m^{2} \cdot 16 n^{4} \cdot 4$

Step 7

Simplify the expression.

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Step 7.1

Multiply $4$ by $16$ .

$m^{2} \cdot 64 n^{4}$

Step 7.2

Move $64$ to the left of $m^{2}$ .

$64 m^{2} n^{4}$