# How do you simplify ((r^-1s^2t^-3)/(r^-2s^0t^1))^-1?

Dec 4, 2016

${r}^{-} 1 {s}^{-} 2 {t}^{4}$ or ${t}^{4} / \left(r {s}^{2}\right)$

#### Explanation:

First, using the rules for exponents you can eliminate the denominator of this problem as follows:

${\left(\frac{{r}^{-} 1 {s}^{2} {t}^{-} 3}{{r}^{-} 2 {s}^{0} {t}^{1}}\right)}^{-} 1 \to {\left({r}^{- 1 - - 2} {s}^{2 - 0} {t}^{- 3 - 1}\right)}^{-} 1 \to$

${\left({r}^{- 1 + 2} {s}^{2} {t}^{-} 4\right)}^{-} 1 \to {\left({r}^{1} {s}^{2} {t}^{-} 4\right)}^{-} 1$

Now that we have simplified the fraction we can apply the exponent to the entire term continuing to use the rules for exponents:

${\left({r}^{1} {s}^{2} {t}^{-} 4\right)}^{-} 1 \to {r}^{1 \cdot - 1} {s}^{2 \cdot - 1} {t}^{- 4 \cdot - 1} \to {r}^{-} 1 {s}^{-} 2 {t}^{4}$ or

${t}^{4} / \left({r}^{1} {s}^{2}\right) \to {t}^{4} / \left(r {s}^{2}\right)$