How do find the quotient of $\frac{- 300 x^{5} y^{4}}{x y^{2}}$ $(-300x^5y^4)/(xy^2)$ ?

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Answer 1 · 2018-03-18T14:29:42

See a solution process below:

First, rewrite the expression as:

$- 300 (\frac{x^{5}}{x}) (\frac{y^{4}}{y^{2}})$ $-300(x^5/x)(y^4/y^2)$

Next, use this rule for exponents to rewrite the $x$ $x$ term in the denominator:

$a = a^{1}$ $a = a^color(blue)(1)$

$- 300 (\frac{x^{5}}{x^{1}}) (\frac{y^{4}}{y^{2}})$ $-300(x^5/x^color(blue)(1))(y^4/y^2)$

Now, use this rule for exponents to find the quotient:

$\frac{x^{a}}{x^{b}} = x^{a - b}$ $x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))$

$- 300 (\frac{x^{5}}{x^{1}}) (\frac{y^{4}}{y^{2}}) \Rightarrow$ $-300(x^color(red)(5)/x^color(blue)(1))(y^color(red)(4)/y^color(blue)(2)) =>$

$- 300 x^{5 - 1} y^{4 - 2} \Rightarrow$ $-300x^(color(red)(5)-color(blue)(1))y^(color(red)(4)-color(blue)(2)) =>$

$- 300 x^{4} y^{2}$ $-300x^4y^2$

How do find the quotient of −300x5y4xy2(-300x^5y^4)/(xy^2)?