Finite Math Examples

${(\frac{m^{4} \cdot m^{- 7}}{m^{2}})}^{\frac{1}{3}}$

Step 1

Multiply $m^{4}$ by $m^{- 7}$ by adding the exponents.

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Step 1.1

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

${(\frac{m^{4 - 7}}{m^{2}})}^{\frac{1}{3}}$

Step 1.2

Subtract $7$ from $4$ .

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

Step 2

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

${(\frac{1}{m^{2} m^{3}})}^{\frac{1}{3}}$

Step 3

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

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Step 3.1

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

${(\frac{1}{m^{2 + 3}})}^{\frac{1}{3}}$

Step 3.2

Add $2$ and $3$ .

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

Step 4

Apply the product rule to $\frac{1}{m^{5}}$ .

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

Step 5

One to any power is one.

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

Step 6

Multiply the exponents in ${(m^{5})}^{\frac{1}{3}}$ .

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Step 6.1

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

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

Step 6.2

Combine $5$ and $\frac{1}{3}$ .

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