Question #fb92a

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Question #fb92a

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Answer 1 · 2017-02-19T03:11:43

If the question is to simplify this expression and ensure there are no negative exponents then see the solution process below:

$\frac{- 25 m^{5} n^{- 5}}{5 m^{- 4} n^{- 2}}$ $(-25m^5n^-5)/(5m^-4n^-2)$

Explanation:

First, we can simplify the constants:

$\frac{- 25 m^{5} n^{- 5}}{5 m^{- 4} n^{- 2}} = \frac{- 5 m^{5} n^{- 5}}{m^{- 4} n^{- 2}}$ $(color(red)(-25)m^5n^-5)/(color(blue)(5)m^-4n^-2) = (-5m^5n^-5)/(m^-4n^-2)$

We can now use these two rules of exponents to simplify the $m$ $m$ and $n$ $n$ terms:

$\frac{x^{a}}{x^{b}} = x^{a - b}$ $x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))$ and $\frac{x^{a}}{x^{b}} = \frac{1}{x^{b - a}}$ $x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))$

$\frac{- 5 m^{5} n^{- 5}}{m^{- 4} n^{- 2}} = \frac{- 5 m^{5 - - 4}}{n^{- 2 - - 5}} = \frac{- 5 m^{5 + 4}}{n^{- 2 + 5}} = \frac{- 5 m^{9}}{n^{3}}$ $(-5m^color(red)(5)n^color(red)(-5))/(m^color(blue)(-4)n^color(blue)(-2)) = (-5m^(color(red)(5)-color(blue)(-4)))/n^(color(blue)(-2)-color(red)(-5)) = (-5m^(color(red)(5)+color(blue)(4)))/n^(color(blue)(-2)+color(red)(5)) = (-5m^9)/n^3$

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Question #fb92a

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