Basic Math Examples

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

Step 1

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

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

Step 2

Combine $2$ and $\frac{1}{m^{3}}$ .

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

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.1

Apply the product rule to $- m n$ .

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

Step 3.2

Apply the product rule to $- m$ .

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

Step 4

Simplify the expression.

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Step 4.1

Rewrite using the commutative property of multiplication.

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

Step 4.2

Raise $- 1$ to the power of $3$ .

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

Step 5

Cancel the common factor of $m^{3}$ .

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Step 5.1

Move the leading negative in $- \frac{2}{m^{3}}$ into the numerator.

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

Step 5.2

Factor $m^{3}$ out of $m^{3} n^{3}$ .

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

Step 5.3

Cancel the common factor.

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

Step 5.4

Rewrite the expression.

$- 2 n^{3}$