Answer
$8x$
Work Step by Step
Using the laws of exponents, the given expression, $
(2x^3)(4x^{-2})
,$ is equivalent to
\begin{array}{l}\require{cancel}
(2)(4)x^{3+(-2)}
\\\\=
8x^{3-2}
\\\\=
8x^{1}
\\\\=
8x
.\end{array}
For more complicated problems, it is helpful to remember that you can flip the location of numbers with negative exponents. In other words, you can move numbers with a negative exponent that are in the numerator to the denominator, and you can move numbers with a negative exponent in the denominator to the numerator.
