# How do you simplify (2hj^2k^-2*h^4j^-1k^4)^0/(2h^-3j^-4k^-2) and write it using only positive exponents?

Aug 24, 2017

See a solution process below:

#### Explanation:

First, we can simplify the numerator using this rule of exponents"

${a}^{\textcolor{red}{0}} = 1$

${\left(2 h {j}^{2} {k}^{-} 2 \cdot {h}^{4} {j}^{-} 1 {k}^{4}\right)}^{\textcolor{red}{0}} / \left(2 {h}^{-} 3 {j}^{-} 4 {k}^{-} 2\right) \implies$

$\frac{1}{2 {h}^{-} 3 {j}^{-} 4 {k}^{-} 2}$

Now, we can use this rule for exponents to eliminate the negative exponents:

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

$\frac{1}{2 {h}^{\textcolor{red}{- 3}} {j}^{\textcolor{red}{- 4}} {k}^{\textcolor{red}{- 2}}} \implies$

$\frac{{h}^{\textcolor{red}{- - 3}} {j}^{\textcolor{red}{- - 4}} {k}^{\textcolor{red}{- - 2}}}{2} \implies$

$\frac{{h}^{\textcolor{red}{3}} {j}^{\textcolor{red}{4}} {k}^{\textcolor{red}{2}}}{2}$