# How do you use the laws of exponents to simplify the expression (-48x^4y^5z^2)/ (6x^2y^6z^4)?

##### 1 Answer
May 17, 2015

The answer is : $- \frac{8 {x}^{2}}{y {z}^{2}}$

Let's separate your fraction :

$\frac{- 48 {x}^{4} {y}^{5} {z}^{2}}{6 {x}^{2} {y}^{6} {z}^{4}} = - \frac{48}{6} \cdot {x}^{4} / {x}^{2} \cdot {y}^{5} / {y}^{6} \cdot {z}^{2} / {z}^{4}$.

Now, we will use the laws of exponents to simplify the last fractions :

$- \frac{48}{6} \cdot {x}^{4} / {x}^{2} \cdot {y}^{5} / {y}^{6} \cdot {z}^{2} / {z}^{4} = - 8 \cdot {x}^{4 - 2} \cdot {y}^{5 - 6} \cdot {z}^{2 - 4}$

$= - 8 \cdot {x}^{2} \cdot {y}^{- 1} \cdot {z}^{- 2} = - 8 \cdot {x}^{2} \cdot \left(\frac{1}{y}\right) \cdot \left(\frac{1}{z} ^ 2\right)$

$= - \frac{8 {x}^{2}}{y {z}^{2}}$