Basic Math Examples

$4 a^{- 1} b^{- 3} (\frac{- a^{3}}{- (b^{2})})$

Step 1

Cancel the common factor of $b^{- 3}$ .

Tap for more steps...

Step 1.1

Factor $b^{- 3}$ out of $4 a^{- 1} b^{- 3}$ .

$b^{- 3} (4 a^{- 1}) \frac{- a^{3}}{- b^{2}}$

Step 1.2

Factor $b^{- 3}$ out of $- b^{2}$ .

$b^{- 3} (4 a^{- 1}) \frac{- a^{3}}{b^{- 3} (- b^{5})}$

Step 1.3

Cancel the common factor.

$b^{- 3} (4 a^{- 1}) \frac{- a^{3}}{b^{- 3} (- b^{5})}$

Step 1.4

Rewrite the expression.

$4 a^{- 1} \frac{- a^{3}}{- b^{5}}$

Step 2

Combine $4$ and $\frac{- a^{3}}{- b^{5}}$ .

$a^{- 1} \frac{4 (- a^{3})}{- b^{5}}$

Step 3

Multiply $- 1$ by $4$ .

$a^{- 1} \frac{- 4 a^{3}}{- b^{5}}$

Step 4

Combine $a^{- 1}$ and $\frac{- 4 a^{3}}{- b^{5}}$ .

$\frac{a^{- 1} (- 4 a^{3})}{- b^{5}}$

Step 5

Multiply $a^{- 1}$ by $a^{3}$ by adding the exponents.

Tap for more steps...

Step 5.1

Move $a^{3}$ .

$\frac{a^{3} a^{- 1} \cdot - 4}{- b^{5}}$

Step 5.2

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

$\frac{a^{3 - 1} \cdot - 4}{- b^{5}}$

Step 5.3

Subtract $1$ from $3$ .

$\frac{a^{2} \cdot - 4}{- b^{5}}$

Step 6

Move $- 4$ to the left of $a^{2}$ .

$\frac{- 4 \cdot a^{2}}{- b^{5}}$

Step 7

Dividing two negative values results in a positive value.

$\frac{4 a^{2}}{b^{5}}$