Algebra Examples

$- m^{2} \cdot 4 r^{3} \cdot 12 r^{- 4} \cdot 5 m$

Step 1

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

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Step 1.1

Move $m$ .

$- (m \cdot m^{2}) \cdot (4 r^{3}) \cdot (12 r^{- 4}) \cdot 5$

Step 1.2

Multiply $m$ by $m^{2}$ .

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Step 1.2.1

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

$- (m^{1} m^{2}) \cdot (4 r^{3}) \cdot (12 r^{- 4}) \cdot 5$

Step 1.2.2

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

$- m^{1 + 2} \cdot (4 r^{3}) \cdot (12 r^{- 4}) \cdot 5$

Step 1.3

Add $1$ and $2$ .

$- m^{3} \cdot (4 r^{3}) \cdot (12 r^{- 4}) \cdot 5$

Step 2

Multiply $r^{3}$ by $r^{- 4}$ by adding the exponents.

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Step 2.1

Move $r^{- 4}$ .

$- m^{3} \cdot (4 (r^{- 4} r^{3})) \cdot 12 \cdot 5$

Step 2.2

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

$- m^{3} \cdot (4 r^{- 4 + 3}) \cdot 12 \cdot 5$

Step 2.3

Add $- 4$ and $3$ .

$- m^{3} \cdot (4 r^{- 1}) \cdot 12 \cdot 5$

Step 3

Rewrite using the commutative property of multiplication.

$- 1 \cdot 4 m^{3} r^{- 1} \cdot 12 \cdot 5$

Step 4

Multiply $- 1$ by $4$ .

$- 4 m^{3} r^{- 1} \cdot 12 \cdot 5$

Step 5

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

$- 4 m^{3} \frac{1}{r} \cdot 12 \cdot 5$

Step 6

Multiply $- 4 m^{3} \frac{1}{r}$ .

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Step 6.1

Combine $- 4$ and $\frac{1}{r}$ .

$m^{3} \frac{- 4}{r} \cdot 12 \cdot 5$

Step 6.2

Combine $m^{3}$ and $\frac{- 4}{r}$ .

$\frac{m^{3} \cdot - 4}{r} \cdot 12 \cdot 5$

Step 7

Move $- 4$ to the left of $m^{3}$ .

$\frac{- 4 \cdot m^{3}}{r} \cdot 12 \cdot 5$

Step 8

Move the negative in front of the fraction.

$- \frac{4 \cdot m^{3}}{r} \cdot 12 \cdot 5$

Step 9

Multiply $- \frac{4 m^{3}}{r} \cdot 12$ .

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Step 9.1

Multiply $12$ by $- 1$ .

$- 12 \frac{4 m^{3}}{r} \cdot 5$

Step 9.2

Combine $- 12$ and $\frac{4 m^{3}}{r}$ .

$\frac{- 12 (4 m^{3})}{r} \cdot 5$

Step 9.3

Multiply $4$ by $- 12$ .

$\frac{- 48 m^{3}}{r} \cdot 5$

Step 10

Move the negative in front of the fraction.

$- \frac{48 m^{3}}{r} \cdot 5$

Step 11

Multiply $- \frac{48 m^{3}}{r} \cdot 5$ .

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Step 11.1

Multiply $5$ by $- 1$ .

$- 5 \frac{48 m^{3}}{r}$

Step 11.2

Combine $- 5$ and $\frac{48 m^{3}}{r}$ .

$\frac{- 5 (48 m^{3})}{r}$

Step 11.3

Multiply $48$ by $- 5$ .

$\frac{- 240 m^{3}}{r}$

Step 12

Move the negative in front of the fraction.

$- \frac{240 m^{3}}{r}$