# How do you simplify (5x^-7y^-3)/(30y^9x^-4)?

May 16, 2018

$= \frac{1}{6 {x}^{3} {y}^{12}}$

#### Explanation:

Recall the law of indices concerning negative indices:

${x}^{-} m = \frac{1}{x} ^ m \text{ } \mathmr{and} \frac{1}{x} ^ - m = {x}^{m}$

Apply these laws to the highlighted indices below

$\frac{5 \textcolor{b l u e}{{x}^{-} 7} \textcolor{m a \ge n t a}{{y}^{-} 3}}{30 {y}^{9} \textcolor{g r e e n}{{x}^{-} 4}}$

=(cancel5color(green)(x^4))/(cancel30_6 y^9color(blue)(x^7)color(magenta)(y^3)

$= \frac{1}{6 {x}^{3} {y}^{12}}$

May 16, 2018

$\frac{1}{6 {y}^{12} {x}^{3}}$
The reason is because negative exponents in the numerator go to the denominator and is the same concept for negative exponents in the denominator. then you divide the remaining exponents (aka subtract the exponents) for example ${x}^{4} / {x}^{7} = \frac{1}{x} ^ 3$