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Q35.

Expert-verified
Found in: Page 227

### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903

# Simplify $\frac{-12{m}^{4}{n}^{8}\left({m}^{3}{n}^{2}\right)}{36{m}^{3}n}$ assuming that no variable equal to 0 .

The simplified value of expression is $-\frac{{m}^{4}{n}^{9}}{3}$.

See the step by step solution

## Step 1. Write down the given expression.

The given expressiomn to simplify is $\frac{-12{m}^{4}{n}^{8}\left({m}^{3}{n}^{2}\right)}{36{m}^{3}n}$ .

## Step 2. Simplify the given expression.

Simplifying $\frac{-12{m}^{4}{n}^{8}\left({m}^{3}{n}^{2}\right)}{36{m}^{3}n}$ gives,

$\begin{array}{c}\frac{-12{m}^{4}{n}^{8}\left({m}^{3}{n}^{2}\right)}{36{m}^{3}n}=\frac{\left(-12\right)\left({m}^{4}{n}^{8}\right)\left({m}^{3}{n}^{2}\right)}{\left(36\right)\left({m}^{3}n\right)}\\ =-\frac{\left({m}^{4}{n}^{8}\right)\left({m}^{3}{n}^{2}\right)}{3\left({m}^{3}n\right)}\\ =-\frac{\left({m}^{4+3-3}\right)\left({n}^{8+2-1}\right)}{3}....\left(\text{Using}\frac{{\left(x\right)}^{a}{\left(x\right)}^{b}}{{\left(x\right)}^{c}}={x}^{a+b-c}\right)\\ =-\frac{{m}^{4}{n}^{9}}{3}\end{array}$

## Step 3. Conclusion.

The simplified value of expression is $-\frac{{m}^{4}{n}^{9}}{3}$ .