Simplify (-1/2a^7b^3)(5a^2b^2)

$(- \frac{1}{2} a^{7} b^{3}) (5 a^{2} b^{2})$

Step 1

Multiply $a^{7}$ by $a^{2}$ by adding the exponents.

Move $a^{2}$ .

$- \frac{1}{2} \cdot (a^{2} a^{7} b^{3}) (5 b^{2})$

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

$- \frac{1}{2} \cdot (a^{2 + 7} b^{3}) (5 b^{2})$

Add $2$ and $7$ .

$- \frac{1}{2} \cdot (a^{9} b^{3}) (5 b^{2})$

Step 2

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

Move $b^{2}$ .

$- \frac{1}{2} \cdot (a^{9} (b^{2} b^{3})) \cdot 5$

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

$- \frac{1}{2} \cdot (a^{9} b^{2 + 3}) \cdot 5$

Add $2$ and $3$ .

$- \frac{1}{2} \cdot (a^{9} b^{5}) \cdot 5$

Step 3

Multiply $- \frac{1}{2} (a^{9} b^{5})$ .

Combine $a^{9}$ and $\frac{1}{2}$ .

$- \frac{a^{9}}{2} b^{5} \cdot 5$

Combine $b^{5}$ and $\frac{a^{9}}{2}$ .

$- \frac{b^{5} a^{9}}{2} \cdot 5$

Step 4

Multiply $- \frac{b^{5} a^{9}}{2} \cdot 5$ .

Multiply $5$ by $- 1$ .

$- 5 \frac{b^{5} a^{9}}{2}$

Combine $- 5$ and $\frac{b^{5} a^{9}}{2}$ .

$\frac{- 5 (b^{5} a^{9})}{2}$

Step 5

Move the negative in front of the fraction.

$- \frac{5 b^{5} a^{9}}{2}$