Algebra 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

Move the negative in front of the fraction.

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

Step 6

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 7

Multiply $\frac{1}{n}$ by $\frac{9}{m^{5}}$ .

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

Step 8

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

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Step 8.1

Multiply $2$ by $- 1$ .

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

Step 8.2

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

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

Step 8.3

Multiply $- 2$ by $9$ .

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

Step 9

Move the negative in front of the fraction.

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