# How do you simplify (4a^3 b^2) (4a^2 b^5)?

Mar 19, 2018

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$\left(4 \cdot 4\right) \left({a}^{3} \cdot {a}^{2}\right) \left({b}^{2} \cdot {b}^{5}\right) \implies$

$16 \left({a}^{3} \cdot {a}^{2}\right) \left({b}^{2} \cdot {b}^{5}\right)$

Now, use this rule for exponents to simplify the $a$ and $b$ terms:

${x}^{\textcolor{red}{a}} \times {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

$16 \left({a}^{\textcolor{red}{3}} \cdot {a}^{\textcolor{b l u e}{2}}\right) \left({b}^{\textcolor{red}{2}} \cdot {b}^{\textcolor{b l u e}{5}}\right) \implies$

$16 {a}^{\textcolor{red}{3} + \textcolor{b l u e}{2}} {b}^{\textcolor{red}{2} + \textcolor{b l u e}{5}} \implies$

$16 {a}^{5} {b}^{7}$