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

Apr 7, 2017

3/(4y^13

#### Explanation:

You can get rid of the negative index by using one of the laws of indices: ${x}^{-} m = \frac{1}{x} ^ m$
The whole bracket moves to the denominator and the index becomes positive.

$\frac{\left(3 {y}^{3}\right) \textcolor{red}{{\left(2 {y}^{2}\right)}^{-} 2}}{{y}^{4}} ^ 3 = \frac{3 {y}^{3}}{\textcolor{red}{{\left(2 {y}^{2}\right)}^{2}} {\left({y}^{4}\right)}^{3}}$

Now use the power law of indices ${\left({x}^{m}\right)}^{n} = {x}^{m} n$

(3y^3)/((4y^4 y^12)

Simplifying gives:

3/(4y^13