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jmc

algebra intermediate

Problem

Simplify

\frac{4}{3 x ^{- 3}} \cdot \frac{3 x ^{2}}{2}

.

Solution

First, we recognize that

\frac{4}{3 x ^{- 3}}

can be rewritten as

\frac{4 x ^{3}}{3}

. Thus, we have

\frac{4}{3 x ^{- 3}} \cdot \frac{3 x ^{2}}{2} = \frac{4 x ^{3}}{3} \cdot \frac{3 x ^{2}}{2} = \frac{( 4 \cdot 3 ) ( x ^{3} \cdot x ^{2} )}{3 \cdot 2} = 2 x^{3 + 2} = 2 x^{5} .

Final answer

2x^5