Basic Math Examples

${({(5 m^{4} n^{- 2})}^{- 1})}^{- 3}$

Step 1

Multiply the exponents in ${({(5 m^{4} n^{- 2})}^{- 1})}^{- 3}$ .

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Step 1.1

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

${(5 m^{4} n^{- 2})}^{- - 3}$

Step 1.2

Multiply $- 1$ by $- 3$ .

${(5 m^{4} n^{- 2})}^{3}$

Step 2

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

${(5 m^{4} \frac{1}{n^{2}})}^{3}$

Step 3

Multiply $5 m^{4} \frac{1}{n^{2}}$ .

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Step 3.1

Combine $5$ and $\frac{1}{n^{2}}$ .

${(m^{4} \frac{5}{n^{2}})}^{3}$

Step 3.2

Combine $m^{4}$ and $\frac{5}{n^{2}}$ .

${(\frac{m^{4} \cdot 5}{n^{2}})}^{3}$

Step 4

Move $5$ to the left of $m^{4}$ .

${(\frac{5 \cdot m^{4}}{n^{2}})}^{3}$

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 $\frac{5 m^{4}}{n^{2}}$ .

$\frac{{(5 m^{4})}^{3}}{{(n^{2})}^{3}}$

Step 5.2

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

$\frac{5^{3} {(m^{4})}^{3}}{{(n^{2})}^{3}}$

Step 6

Simplify the numerator.

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Step 6.1

Raise $5$ to the power of $3$ .

$\frac{125 {(m^{4})}^{3}}{{(n^{2})}^{3}}$

Step 6.2

Multiply the exponents in ${(m^{4})}^{3}$ .

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Step 6.2.1

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

$\frac{125 m^{4 \cdot 3}}{{(n^{2})}^{3}}$

Step 6.2.2

Multiply $4$ by $3$ .

$\frac{125 m^{12}}{{(n^{2})}^{3}}$

Step 7

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

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Step 7.1

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

$\frac{125 m^{12}}{n^{2 \cdot 3}}$

Step 7.2

Multiply $2$ by $3$ .

$\frac{125 m^{12}}{n^{6}}$