# How do you simplify ((-3)^0 x^4 y^-1) /( x^-1 yz ^-2)?

Jan 26, 2017

#### Answer:

$\frac{{\left(- 3\right)}^{0} {x}^{4} {y}^{-} 1}{{x}^{-} 1 y {z}^{-} 2} = \frac{{x}^{5} {z}^{2}}{y} ^ 2$

#### Explanation:

Some rules which apply to indices:

${a}^{0} \equiv 1 ,$ $\text{given}$ $a \ne 0$

${a}^{m} / {a}^{n} \equiv {a}^{m - n} ,$ $\text{given}$ $m - n > 0$ $\text{where}$ $a = 0$

${a}^{- n} \equiv \frac{1}{{a}^{n}} ,$ $\text{given}$ $a \ne 0$

$- {3}^{0} = 1$

${x}^{4} / {x}^{-} 1 = {x}^{4 - - 1} = {x}^{5}$

${y}^{-} \frac{1}{y} = {y}^{- 1 - 1} = {y}^{-} 2$

$\frac{1 \left({z}^{0}\right)}{z} ^ - 2 = {z}^{0 - - 2} = {z}^{2}$

$\frac{{\left(- 3\right)}^{0} {x}^{4} {y}^{-} 1}{{x}^{-} 1 y {z}^{-} 2} = {x}^{5} {y}^{-} 2 {z}^{2} = {x}^{5} \frac{1}{y} ^ 2 {z}^{2} = \frac{{x}^{5} {z}^{2}}{y} ^ 2$