Simplify the given expression. Write answers with positive exponents.

$\frac{m^2 n^3}{a^2 c^{-3}} \cdot \frac{a^{-7} n^{-2}}{m^2 c^4}$

Solutions

Verified$\begin{align*} \frac{m^2n^3}{a^2c^{-3}}\cdot \frac{a^{-7}n^{-2}}{m^2c^4} &= \frac{m^2}{m^2}\cdot \frac{a^{-7}}{a^2} \cdot \frac{1}{c^{-3}c^4} \cdot n^3n^{-2} \tag{Associative property}\\ &= \frac{m^2}{m^2}\cdot \frac{a^{-7}}{a^2} \cdot \frac{1}{c^{-3+4}} \cdot n^{3+(-2)} \tag{Product rule}\\ &= \frac{m^2}{m^2}\cdot \frac{a^{-7}}{a^2} \cdot \frac{1}{c^{-3+4}} \cdot n^{3-2} \tag{Change signs}\\ &= \frac{m^2}{m^2}\cdot \frac{a^{-7}}{a^2} \cdot \frac{1}{c^1} \cdot n^1 \tag{Simplify}\\ &= \frac{m^2}{m^2}\cdot \frac{a^{-7}}{a^2} \cdot \frac{n}{c} \tag{Simplify}\\ &= m^{2-2} \cdot a^{-7-2} \cdot \frac{n}{c} \tag{Quotient rule}\\ &= m^0 \cdot a^{-9} \cdot \frac{n}{c} \tag{Simplify}\\ &= 1 \cdot a^{-9} \cdot \frac{n}{c} \tag{Zero exponent rule}\\ &= \frac{1}{a^9} \cdot \frac{n}{c} \tag{Negative exponent rule}\\ &= \boxed{\frac{n}{a^9c}} \tag{Simplify} \end{align*}$

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