Answer
$\dfrac{79}{6}$
Work Step by Step
Recall, in order to solve problems involving order of operations, we use the PEMDAS rule.
First Priority: P - parentheses and other grouping symbols (including fraction bars)
Second Priority: E - exponents
Third Priority: M/D - Multiplication or division, whichever comes first from the left to the right
Fourth Priority: A/S - Addition or subtraction, whichever comes first from the left to the right
We follow order of operations to obtain that the expression, $
\dfrac{-5(2-3)^3}{2}-\dfrac{4(2-4)^3}{3}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{-5(-1)^3}{2}-\dfrac{4(-2)^3}{3}
\\\\=
\dfrac{-5(-1)(-1)(-1)}{2}-\dfrac{4(-2)(-2)(-2)}{3}
\\\\=
\dfrac{5}{2}-\dfrac{-32}{3}
\\\\=
\dfrac{15}{6}+\dfrac{64}{6}
\\\\=
\dfrac{79}{6}
.\end{array}
