Answer
$-13$
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{-3(2)^4}{12}+\dfrac{5(-3)^3}{15}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{-3(2)(2)(2)(2)}{12}+\dfrac{5(-3)(-3)(-3)}{15}
\\\\=
\dfrac{-3(2)(2)(2)(2)}{2(2)(3)}+\dfrac{5(-3)(-3)(-3)}{3(5)}
\\\\=
\dfrac{-\cancel{3}(\cancel{2})(\cancel{2})(2)(2)}{\cancel{2}(\cancel{2})(\cancel{3})}+\dfrac{\cancel{5}(-3)(-3)(-\cancel{3})}{\cancel{3}(\cancel{5})}
\\\\=
-4+(-9)
\\\\=
-4-9
\\\\=
-13
.\end{array}
