Algebra Examples

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

Step 1

Rewrite using the commutative property of multiplication.

$4 \cdot 2 r^{- 3} r^{2}$

Step 2

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

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Step 2.1

Move $r^{2}$ .

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

Step 2.2

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

$4 \cdot 2 r^{2 - 3}$

Step 2.3

Subtract $3$ from $2$ .

$4 \cdot 2 r^{- 1}$

Step 3

Multiply $4$ by $2$ .

$8 r^{- 1}$

Step 4

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

$8 \frac{1}{r}$

Step 5

Combine $8$ and $\frac{1}{r}$ .

$\frac{8}{r}$