Algebra Examples

$(12 m n) (- m^{3} n^{- 2} p^{5}) (2 m)$

Step 1

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

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Step 1.1

Move $m^{3}$ .

$12 (m^{3} m) n (- 1 n^{- 2} p^{5}) (2 m)$

Step 1.2

Multiply $m^{3}$ by $m$ .

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Step 1.2.1

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

$12 (m^{3} m^{1}) n (- 1 n^{- 2} p^{5}) (2 m)$

Step 1.2.2

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

$12 m^{3 + 1} n (- 1 n^{- 2} p^{5}) (2 m)$

Step 1.3

Add $3$ and $1$ .

$12 m^{4} n (- 1 n^{- 2} p^{5}) (2 m)$

Step 2

Multiply $m^{4}$ by $m$ by adding the exponents.

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Step 2.1

Move $m$ .

$12 (m \cdot m^{4}) n (- 1 n^{- 2} p^{5}) \cdot 2$

Step 2.2

Multiply $m$ by $m^{4}$ .

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Step 2.2.1

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

$12 (m^{1} m^{4}) n (- 1 n^{- 2} p^{5}) \cdot 2$

Step 2.2.2

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

$12 m^{1 + 4} n (- 1 n^{- 2} p^{5}) \cdot 2$

Step 2.3

Add $1$ and $4$ .

$12 m^{5} n (- 1 n^{- 2} p^{5}) \cdot 2$

Step 3

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

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Step 3.1

Move $n^{- 2}$ .

$12 m^{5} (n^{- 2} n) (- 1 p^{5}) \cdot 2$

Step 3.2

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

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Step 3.2.1

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

$12 m^{5} (n^{- 2} n^{1}) (- 1 p^{5}) \cdot 2$

Step 3.2.2

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

$12 m^{5} n^{- 2 + 1} (- 1 p^{5}) \cdot 2$

Step 3.3

Add $- 2$ and $1$ .

$12 m^{5} n^{- 1} (- 1 p^{5}) \cdot 2$

Step 4

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

$12 m^{5} \frac{1}{n} (- 1 p^{5}) \cdot 2$

Step 5

Multiply $12 m^{5} \frac{1}{n}$ .

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Step 5.1

Combine $12$ and $\frac{1}{n}$ .

$m^{5} \frac{12}{n} (- 1 p^{5}) \cdot 2$

Step 5.2

Combine $m^{5}$ and $\frac{12}{n}$ .

$\frac{m^{5} \cdot 12}{n} (- 1 p^{5}) \cdot 2$

Step 6

Reorder.

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Step 6.1

Rewrite using the commutative property of multiplication.

$- \frac{m^{5} \cdot 12}{n} p^{5} \cdot 2$

Step 6.2

Move $12$ to the left of $m^{5}$ .

$- \frac{12 \cdot m^{5}}{n} p^{5} \cdot 2$

Step 7

Combine $p^{5}$ and $\frac{12 m^{5}}{n}$ .

$- \frac{p^{5} (12 m^{5})}{n} \cdot 2$

Step 8

Move $12$ to the left of $p^{5}$ .

$- \frac{12 \cdot p^{5} m^{5}}{n} \cdot 2$

Step 9

Multiply $- \frac{12 p^{5} m^{5}}{n} \cdot 2$ .

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Step 9.1

Multiply $2$ by $- 1$ .

$- 2 \frac{12 p^{5} m^{5}}{n}$

Step 9.2

Combine $- 2$ and $\frac{12 p^{5} m^{5}}{n}$ .

$\frac{- 2 (12 p^{5} m^{5})}{n}$

Step 9.3

Multiply $12$ by $- 2$ .

$\frac{- 24 (p^{5} m^{5})}{n}$

Step 10

Move the negative in front of the fraction.

$- \frac{24 p^{5} m^{5}}{n}$