How do you simplify \frac { 13x ^ { - 5} y ^ { 0} } { 5^- 3z ^- 10}?

Jan 15, 2018

See a solution process below:

Explanation:

First, use this rule for exponents to simplify the $y$ term:

${a}^{\textcolor{red}{0}} = 1$

$\frac{13 {x}^{-} 5 {y}^{\textcolor{red}{0}}}{{5}^{-} 3 {z}^{-} 10} \implies \frac{13 {x}^{-} 5 \cdot 1}{{5}^{-} 3 {z}^{-} 10} \implies \frac{13 {x}^{-} 5 \cdot 1}{{5}^{-} 3 {z}^{-} 10} \implies \frac{13 {x}^{-} 5}{{5}^{-} 3 {z}^{-} 10}$

Next, we can eliminate the negative exponents in the denominator using this rule of exponents:

$\frac{1}{x} ^ \textcolor{red}{a} = {x}^{\textcolor{red}{- a}}$

$\frac{13 {x}^{-} 5}{{5}^{\textcolor{red}{- 3}} {z}^{\textcolor{red}{- 10}}} \implies \left(13 {x}^{-} 5\right) \left({5}^{\textcolor{red}{- - 3}} {z}^{\textcolor{red}{- - 10}}\right) \implies \left(13 {x}^{-} 5\right) \left({5}^{\textcolor{red}{3}} {z}^{\textcolor{red}{10}}\right) \implies$

$\left(13 {x}^{-} 5\right) \left(125 {z}^{10}\right) \implies \left(13 \times 125\right) \left({x}^{-} 5 {z}^{10}\right) \implies 1625 {x}^{-} 5 {z}^{10}$

Now, we can use this rule for exponents to eliminate the negative exponent for the $x$ term:

${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$

$1625 {x}^{\textcolor{red}{- 5}} {z}^{10} \implies \frac{1625 {z}^{10}}{x} ^ \textcolor{red}{- - 5} \implies \frac{1625 {z}^{10}}{x} ^ 5$