How do you use laws of exponents to simplify (( 10x^4y^2)/(-5x^3y^2)^2)?

Aug 4, 2015

Let's first work the brackets below the division bar:

Explanation:

$= \frac{10 {x}^{4} {y}^{2}}{25 {x}^{6} {y}^{4}} = \frac{2 \cdot \cancel{5} \cdot {\cancel{x}}^{4} \cdot {\cancel{y}}^{2}}{5 \cdot \cancel{5} \cdot {\cancel{x}}^{4} \cdot {x}^{2} \cdot {\cancel{y}}^{2} \cdot {y}^{2}}$

$= \frac{2}{5 {x}^{2} {y}^{2}} \mathmr{and} \frac{2}{5 {\left(x y\right)}^{2}}$

Or you could have done:

$= \frac{10}{{\left(- 5\right)}^{2}} \cdot {x}^{4 - 3 \cdot 2} \cdot {y}^{2 - 2 \cdot 2} = \frac{2}{5} \cdot {x}^{-} 2 \cdot {y}^{-} 2$