Basic Math Examples

$\frac{5 a^{5} b^{4} \cdot (- 4 a^{- 5})}{- 3 b^{- 2}}$

Step 1

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

Tap for more steps...

Step 1.1

Move $a^{- 5}$ .

$\frac{5 (a^{- 5} a^{5}) b^{4} \cdot - 4}{- 3 b^{- 2}}$

Step 1.2

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

$\frac{5 a^{- 5 + 5} b^{4} \cdot - 4}{- 3 b^{- 2}}$

Step 1.3

Add $- 5$ and $5$ .

$\frac{5 a^{0} b^{4} \cdot - 4}{- 3 b^{- 2}}$

Step 2

Simplify $5 a^{0} b^{4} \cdot - 4$ .

$\frac{5 b^{4} \cdot - 4}{- 3 b^{- 2}}$

Step 3

Move $b^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{5 b^{4} \cdot - 4 b^{2}}{- 3}$

Step 4

Multiply $b^{4}$ by $b^{2}$ by adding the exponents.

Tap for more steps...

Step 4.1

Move $b^{2}$ .

$\frac{5 (b^{2} b^{4}) \cdot - 4}{- 3}$

Step 4.2

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

$\frac{5 b^{2 + 4} \cdot - 4}{- 3}$

Step 4.3

Add $2$ and $4$ .

$\frac{5 b^{6} \cdot - 4}{- 3}$

Step 5

Multiply $- 4$ by $5$ .

$\frac{- 20 b^{6}}{- 3}$

Step 6

Dividing two negative values results in a positive value.

$\frac{20 b^{6}}{3}$