# How do you simplify ba^4*(2ba^4)^-3 and write it using only positive exponents?

Feb 17, 2017

The simplified answer is $\frac{1}{8 {b}^{2} {a}^{8}}$.

#### Explanation:

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

In order to simplify this expression, we will need to apply several rules of exponents.

Apply negative power rule a^(-m)=1/am".

$\frac{b {a}^{4}}{2 b {a}^{4}} ^ 3$

Apply power rule ${\left({a}^{m}\right)}^{n} = {a}^{m \cdot n}$.

$\frac{b {a}^{4}}{{2}^{3} {b}^{3} {a}^{12}}$

Simplify ${2}^{3}$.

$\frac{b {a}^{4}}{8 {b}^{3} {a}^{12}}$

Apply quotient rule ${a}^{m} / {a}^{n} = {a}^{m - n}$

$\frac{{b}^{1 - 3} {a}^{4 - 12}}{8}$

Simplify.

$\frac{{b}^{-} 2 {a}^{-} 8}{8}$

Apply negative power rule ${a}^{- m} = \frac{1}{a} ^ m$

$\frac{1}{8 {b}^{2} {a}^{8}}$