Basic Math Examples

$m^{- 9} {(m^{- 1} n)}^{2} n^{8}$

Step 1

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

$\frac{1}{m^{9}} {(m^{- 1} n)}^{2} n^{8}$

Step 2

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

$\frac{1}{m^{9}} {(\frac{1}{m} n)}^{2} n^{8}$

Step 3

Combine $\frac{1}{m}$ and $n$ .

$\frac{1}{m^{9}} {(\frac{n}{m})}^{2} n^{8}$

Step 4

Apply the product rule to $\frac{n}{m}$ .

$\frac{1}{m^{9}} \cdot \frac{n^{2}}{m^{2}} n^{8}$

Step 5

Combine.

$\frac{1 n^{2}}{m^{9} m^{2}} n^{8}$

Step 6

Multiply $n^{2}$ by $1$ .

$\frac{n^{2}}{m^{9} m^{2}} n^{8}$

Step 7

Multiply $m^{9}$ by $m^{2}$ by adding the exponents.

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Step 7.1

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

$\frac{n^{2}}{m^{9 + 2}} n^{8}$

Step 7.2

Add $9$ and $2$ .

$\frac{n^{2}}{m^{11}} n^{8}$

Step 8

Multiply $\frac{n^{2}}{m^{11}} n^{8}$ .

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Step 8.1

Combine $\frac{n^{2}}{m^{11}}$ and $n^{8}$ .

$\frac{n^{2} n^{8}}{m^{11}}$

Step 8.2

Multiply $n^{2}$ by $n^{8}$ by adding the exponents.

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Step 8.2.1

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

$\frac{n^{2 + 8}}{m^{11}}$

Step 8.2.2

Add $2$ and $8$ .

$\frac{n^{10}}{m^{11}}$