Basic Math Examples

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

Step 1

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

${(4 m^{3} m^{2})}^{- 3}$

Step 2

Multiply $m^{3}$ by $m^{2}$ by adding the exponents.

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Step 2.1

Move $m^{2}$ .

${(4 (m^{2} m^{3}))}^{- 3}$

Step 2.2

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

${(4 m^{2 + 3})}^{- 3}$

Step 2.3

Add $2$ and $3$ .

${(4 m^{5})}^{- 3}$

Step 3

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

$\frac{1}{{(4 m^{5})}^{3}}$

Step 4

Simplify the denominator.

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Step 4.1

Apply the product rule to $4 m^{5}$ .

$\frac{1}{4^{3} {(m^{5})}^{3}}$

Step 4.2

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

$\frac{1}{64 {(m^{5})}^{3}}$

Step 4.3

Multiply the exponents in ${(m^{5})}^{3}$ .

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Step 4.3.1

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

$\frac{1}{64 m^{5 \cdot 3}}$

Step 4.3.2

Multiply $5$ by $3$ .

$\frac{1}{64 m^{15}}$