# How do you simplify 4a^3b^2*3a^-4b^-3 and write it using only positive exponents?

Jan 14, 2017

See entire simplification process below:

#### Explanation:

First, we need to group like terms:

$4 {a}^{3} {b}^{2} \cdot 3 {a}^{-} 4 {b}^{-} 3 \to$

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

Now we can use this rule of exponents to combine like terms:

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

$\left(12\right) \left({a}^{3 + - 4}\right) \left({b}^{2 + - 3}\right)$

$12 {a}^{3 - 4} {b}^{2 - 3}$

$12 {a}^{-} 1 {b}^{-} 1$

To eliminate the negative exponent we can use this rule for exponents:

${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$

$\frac{12}{{a}^{- - 1} {b}^{- - 1}}$

$\frac{12}{{a}^{1} {b}^{1}}$

The final rule of exponents we will use to complete the simplification is:

${a}^{\textcolor{red}{1}} = a$

$\frac{12}{a b}$