# How do you simplify (22x^-6*y^4*z^10)/(11x^-2*y^12*z^-5)?

Apr 2, 2015

Let's look at this problem split into fractions:

$\frac{22}{11} \cdot {x}^{-} \frac{6}{x} ^ - 2 \cdot {y}^{4} / {y}^{12} \cdot {z}^{10} / {z}^{-} 5$

When you divide exponents of the same base, you are subtracting the power of the denominator from the power of the numerator:

$2 \cdot {x}^{- 6 + 2} \cdot {y}^{4 - 12} \cdot {z}^{10 + 5}$

$2 {x}^{-} 4 {y}^{-} 8 {z}^{15}$

Sometimes it is preferred to express an answer without negative exponents. Since ${x}^{-} 4$ can be expressed as $\frac{1}{x} ^ 4$ and ${y}^{-} 8$ can be expressed as $\frac{1}{y} ^ 8$:

$2 {x}^{-} 4 {y}^{-} 8 {z}^{15} = \frac{2 {z}^{15}}{{x}^{4} {y}^{8}}$