Algebra Examples

$(- k^{- 4} m^{7}) (3 k^{5} m^{- 1}) (2 k^{- 2} m)$

Step 1

Multiply $k^{- 4}$ by $k^{5}$ by adding the exponents.

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Step 1.1

Move $k^{5}$ .

$- (k^{5} k^{- 4}) m^{7} (3 m^{- 1}) (2 k^{- 2} m)$

Step 1.2

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

$- k^{5 - 4} m^{7} (3 m^{- 1}) (2 k^{- 2} m)$

Step 1.3

Subtract $4$ from $5$ .

$- k^{1} m^{7} (3 m^{- 1}) (2 k^{- 2} m)$

Step 2

Simplify $- k^{1} m^{7} (3 m^{- 1}) (2 k^{- 2} m)$ .

$- k m^{7} (3 m^{- 1}) (2 k^{- 2} m)$

Step 3

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

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Step 3.1

Move $k^{- 2}$ .

$- (k^{- 2} k) m^{7} (3 m^{- 1}) (2 m)$

Step 3.2

Multiply $k^{- 2}$ by $k$ .

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Step 3.2.1

Raise $k$ to the power of $1$ .

$- (k^{- 2} k^{1}) m^{7} (3 m^{- 1}) (2 m)$

Step 3.2.2

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

$- k^{- 2 + 1} m^{7} (3 m^{- 1}) (2 m)$

Step 3.3

Add $- 2$ and $1$ .

$- k^{- 1} m^{7} (3 m^{- 1}) (2 m)$

Step 4

Multiply $m^{7}$ by $m^{- 1}$ by adding the exponents.

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Step 4.1

Move $m^{- 1}$ .

$- k^{- 1} (m^{- 1} m^{7}) \cdot 3 (2 m)$

Step 4.2

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

$- k^{- 1} m^{- 1 + 7} \cdot 3 (2 m)$

Step 4.3

Add $- 1$ and $7$ .

$- k^{- 1} m^{6} \cdot 3 (2 m)$

Step 5

Multiply $m^{6}$ by $m$ by adding the exponents.

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Step 5.1

Move $m$ .

$- k^{- 1} (m \cdot m^{6}) \cdot 3 \cdot 2$

Step 5.2

Multiply $m$ by $m^{6}$ .

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Step 5.2.1

Raise $m$ to the power of $1$ .

$- k^{- 1} (m^{1} m^{6}) \cdot 3 \cdot 2$

Step 5.2.2

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

$- k^{- 1} m^{1 + 6} \cdot 3 \cdot 2$

Step 5.3

Add $1$ and $6$ .

$- k^{- 1} m^{7} \cdot 3 \cdot 2$

Step 6

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

$- \frac{1}{k} m^{7} \cdot 3 \cdot 2$

Step 7

Combine $m^{7}$ and $\frac{1}{k}$ .

$- \frac{m^{7}}{k} \cdot 3 \cdot 2$

Step 8

Multiply $- \frac{m^{7}}{k} \cdot 3$ .

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Step 8.1

Multiply $3$ by $- 1$ .

$- 3 \frac{m^{7}}{k} \cdot 2$

Step 8.2

Combine $- 3$ and $\frac{m^{7}}{k}$ .

$\frac{- 3 m^{7}}{k} \cdot 2$

Step 9

Move the negative in front of the fraction.

$- \frac{3 m^{7}}{k} \cdot 2$

Step 10

Multiply $- \frac{3 m^{7}}{k} \cdot 2$ .

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Step 10.1

Multiply $2$ by $- 1$ .

$- 2 \frac{3 m^{7}}{k}$

Step 10.2

Combine $- 2$ and $\frac{3 m^{7}}{k}$ .

$\frac{- 2 (3 m^{7})}{k}$

Step 10.3

Multiply $3$ by $- 2$ .

$\frac{- 6 m^{7}}{k}$

Step 11

Move the negative in front of the fraction.

$- \frac{6 m^{7}}{k}$