# How do you simplify the expression (4m^4)/(-6m^-2n^5)*(3n^-1)/m^-2 using the properties?

Nov 9, 2017

$= - \frac{2 {m}^{8}}{{n}^{6}}$

#### Explanation:

Some of the laws of indices state:

${x}^{m} \times {x}^{n} = {x}^{m + n}$

${x}^{-} m = \frac{1}{x} ^ m \text{ "and" } \frac{1}{x} ^ - m = {x}^{m}$

This means that negative indices can be changed to positive indices.

$\frac{4 {m}^{4}}{- 6 {m}^{-} 2 {n}^{5}} \times \frac{3 {n}^{-} 1}{{m}^{-} 2}$

$= \frac{4 {m}^{4} {m}^{2}}{- 6 {n}^{5}} \times \frac{3 {m}^{2}}{n} \text{ } \leftarrow$all positive indices

$= \frac{{\cancel{4}}^{2} {m}^{4} {m}^{2}}{- {\cancel{6}}^{\cancel{2}} {n}^{5}} \times \frac{\cancel{3} {m}^{2}}{n}$

$= - \frac{2 {m}^{8}}{{n}^{6}}$