How do you simplify $\frac{8 m^{3} n^{2}}{4 m n^{3}}$ $(8m^3n^2)/(4mn^3)$ ?

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How do you simplify $\frac{8 m^{3} n^{2}}{4 m n^{3}}$ $(8m^3n^2)/(4mn^3)$ ?

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Answer 1 · 2018-03-18T14:53:36

See a solution process below:

Explanation:

First, rewrite the expression as:

$\frac{8}{4} (\frac{m^{3}}{m}) (\frac{n^{2}}{n^{3}}) \Rightarrow$ $8/4(m^3/m)(n^2/n^3) =>$

$2 (\frac{m^{3}}{m}) (\frac{n^{2}}{n^{3}})$ $2(m^3/m)(n^2/n^3)$

Next, use these rules of exponents to rewrite the $m$ $m$ terms:

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

$2 (\frac{m^{3}}{m^{1}}) (\frac{n^{2}}{n^{3}}) \Rightarrow$ $2(m^color(red)(3)/m^color(blue)(1))(n^2/n^3) =>$

$2 m^{3 - 1} (\frac{n^{2}}{n^{3}}) \Rightarrow$ $2m^(color(red)(3)-color(blue)(1))(n^2/n^3) =>$

$2 m^{2} (\frac{n^{2}}{n^{3}})$ $2m^2(n^2/n^3)$

Now, use these rules of exponents to simplify the $n$ $n$ terms:

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

$2 m^{2} (\frac{n^{2}}{n^{3}}) \Rightarrow$ $2m^2(n^color(red)(2)/n^color(blue)(3)) =>$

$2 m^{2} (\frac{1}{n^{3 - 2}}) \Rightarrow$ $2m^2(1/n^(color(blue)(3)-color(red)(2))) =>$

$2 m^{2} (\frac{1}{n^{1}}) \Rightarrow$ $2m^2(1/n^color(red)(1)) =>$

$2 m^{2} (\frac{1}{n}) \Rightarrow$ $2m^2(1/n) =>$

$\frac{2 m^{2}}{n}$ $(2m^2)/n$

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How do you simplify $\frac{8 m^{3} n^{2}}{4 m n^{3}}$ $(8m^3n^2)/(4mn^3)$ ?

1 Answer

Explanation:

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How do you simplify $\frac{8 m^{3} n^{2}}{4 m n^{3}}$ $(8m^3n^2)/(4mn^3)$ ?