Basic Math Examples

$9 m^{- 2} n^{5} \cdot (2 m^{- 3} n^{- 6})$

Step 1

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

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Step 1.1

Move $m^{- 3}$ .

$9 (m^{- 3} m^{- 2}) n^{5} \cdot (2 n^{- 6})$

Step 1.2

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

$9 m^{- 3 - 2} n^{5} \cdot (2 n^{- 6})$

Step 1.3

Subtract $2$ from $- 3$ .

$9 m^{- 5} n^{5} \cdot (2 n^{- 6})$

Step 2

Multiply $n^{5}$ by $n^{- 6}$ by adding the exponents.

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Step 2.1

Move $n^{- 6}$ .

$9 m^{- 5} (n^{- 6} n^{5}) \cdot 2$

Step 2.2

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

$9 m^{- 5} n^{- 6 + 5} \cdot 2$

Step 2.3

Add $- 6$ and $5$ .

$9 m^{- 5} n^{- 1} \cdot 2$

Step 3

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

$9 \frac{1}{m^{5}} n^{- 1} \cdot 2$

Step 4

Combine $9$ and $\frac{1}{m^{5}}$ .

$\frac{9}{m^{5}} n^{- 1} \cdot 2$

Step 5

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

$\frac{9}{m^{5}} \cdot \frac{1}{n} \cdot 2$

Step 6

Combine.

$\frac{9 \cdot 1}{m^{5} n} \cdot 2$

Step 7

Multiply $9$ by $1$ .

$\frac{9}{m^{5} n} \cdot 2$

Step 8

Multiply $\frac{9}{m^{5} n} \cdot 2$ .

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Step 8.1

Combine $\frac{9}{m^{5} n}$ and $2$ .

$\frac{9 \cdot 2}{m^{5} n}$

Step 8.2

Multiply $9$ by $2$ .

$\frac{18}{m^{5} n}$