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

Feb 5, 2017

See the entire simplification process below:

#### Explanation:

First, use the rule of exponents to simplify the term in parenthesis in the numerator: ${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

$\frac{{\left({x}^{\textcolor{red}{- 3}}\right)}^{\textcolor{b l u e}{4}} {x}^{4}}{2 {x}^{-} 3} \to \frac{{x}^{\textcolor{red}{- 3} \times \textcolor{b l u e}{4}} {x}^{4}}{2 {x}^{-} 3} \to \frac{{x}^{-} 12 {x}^{4}}{2 {x}^{-} 3}$

Next, use this rule for exponents to simplify the numerator:

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

$\frac{{x}^{\textcolor{red}{- 12}} {x}^{\textcolor{b l u e}{4}}}{2 {x}^{-} 3} \to {x}^{\textcolor{red}{- 12} + \textcolor{b l u e}{4}} / \left(2 {x}^{-} 3\right) \to {x}^{-} \frac{8}{2 {x}^{-} 3}$

Now, use this rule of exponents to complete the simplification using only positive exponents: ${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = \frac{1}{x} ^ \left(\textcolor{b l u e}{b} - \textcolor{red}{a}\right)$

${x}^{\textcolor{red}{- 8}} / \left(2 {x}^{\textcolor{b l u e}{- 3}}\right) \to \frac{1}{2 {x}^{\textcolor{b l u e}{- 3} - \textcolor{red}{- 8}}} \to \frac{1}{2 {x}^{\textcolor{b l u e}{- 3} + \textcolor{red}{8}}} \to \frac{1}{2 {x}^{5}}$

Feb 5, 2017

$\frac{1}{2 {x}^{5}}$

#### Explanation:

$\frac{{\left({x}^{-} 3\right)}^{4} {x}^{4}}{2 {x}^{-} 3} = \frac{{x}^{-} 12 \cdot {x}^{4}}{2 {x}^{-} 3} = {x}^{-} \frac{8}{2 {x}^{-} 3} = \frac{{x}^{-} 5 \cdot \cancel{{x}^{-} 3}}{2 \cdot \cancel{{x}^{-} 3}} = {x}^{-} \frac{5}{2} = \frac{1}{2 {x}^{5}}$ [Ans]