Basic Math Examples

${(4 m^{6} m^{- 3})}^{3} \div m^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{{(4 m^{6} m^{- 3})}^{3}}{m^{2}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $4 m^{6} m^{- 3}$ .

$\frac{{(4 m^{6})}^{3} {(m^{- 3})}^{3}}{m^{2}}$

Step 2.2

Apply the product rule to $4 m^{6}$ .

$\frac{4^{3} {(m^{6})}^{3} {(m^{- 3})}^{3}}{m^{2}}$

Step 2.3

Raise $4$ to the power of $3$ .

$\frac{64 {(m^{6})}^{3} {(m^{- 3})}^{3}}{m^{2}}$

Step 2.4

Multiply the exponents in ${(m^{6})}^{3}$ .

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Step 2.4.1

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

$\frac{64 m^{6 \cdot 3} {(m^{- 3})}^{3}}{m^{2}}$

Step 2.4.2

Multiply $6$ by $3$ .

$\frac{64 m^{18} {(m^{- 3})}^{3}}{m^{2}}$

Step 2.5

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

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Step 2.5.1

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

$\frac{64 m^{18} m^{- 3 \cdot 3}}{m^{2}}$

Step 2.5.2

Multiply $- 3$ by $3$ .

$\frac{64 m^{18} m^{- 9}}{m^{2}}$

Step 2.6

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

$\frac{64 m^{18} \frac{1}{m^{9}}}{m^{2}}$

Step 2.7

Combine exponents.

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Step 2.7.1

Combine $64$ and $\frac{1}{m^{9}}$ .

$\frac{m^{18} \frac{64}{m^{9}}}{m^{2}}$

Step 2.7.2

Combine $m^{18}$ and $\frac{64}{m^{9}}$ .

$\frac{\frac{m^{18} \cdot 64}{m^{9}}}{m^{2}}$

Step 2.8

Reduce the expression by cancelling the common factors.

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Step 2.8.1

Reduce the expression $\frac{m^{18} \cdot 64}{m^{9}}$ by cancelling the common factors.

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Step 2.8.1.1

Factor $m^{9}$ out of $m^{18} \cdot 64$ .

$\frac{\frac{m^{9} (m^{9} \cdot 64)}{m^{9}}}{m^{2}}$

Step 2.8.1.2

Multiply by $1$ .

$\frac{\frac{m^{9} (m^{9} \cdot 64)}{m^{9} \cdot 1}}{m^{2}}$

Step 2.8.1.3

Cancel the common factor.

$\frac{\frac{m^{9} (m^{9} \cdot 64)}{m^{9} \cdot 1}}{m^{2}}$

Step 2.8.1.4

Rewrite the expression.

$\frac{\frac{m^{9} \cdot 64}{1}}{m^{2}}$

Step 2.8.2

Divide $m^{9} \cdot 64$ by $1$ .

$\frac{m^{9} \cdot 64}{m^{2}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $m^{9}$ and $m^{2}$ .

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Step 3.1.1

Factor $m^{2}$ out of $m^{9} \cdot 64$ .

$\frac{m^{2} (m^{7} \cdot 64)}{m^{2}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Multiply by $1$ .

$\frac{m^{2} (m^{7} \cdot 64)}{m^{2} \cdot 1}$

Step 3.1.2.2

Cancel the common factor.

$\frac{m^{2} (m^{7} \cdot 64)}{m^{2} \cdot 1}$

Step 3.1.2.3

Rewrite the expression.

$\frac{m^{7} \cdot 64}{1}$

Step 3.1.2.4

Divide $m^{7} \cdot 64$ by $1$ .

$m^{7} \cdot 64$

Step 3.2

Move $64$ to the left of $m^{7}$ .

$64 m^{7}$