Answer
$4$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the order of operations to simplify the given expression, $
\dfrac{(-2)^3+4^2}{2\cdot3-5^2+3\cdot7}
.$
$\bf{\text{Solution Details:}}$
Using the order of operations, $PEMDAS$ (Parenthesis, Exponent, Multiplication/Division, Addition/Subtraction), then the given expression simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(-2)^3+4^2}{2\cdot3-5^2+3\cdot7}
\\\\=
\dfrac{-8+16}{2\cdot3-25+3\cdot7}
\\\\=
\dfrac{-8+16}{6-25+21}
\\\\=
\dfrac{8}{-19+21}
\\\\=
\dfrac{8}{2}
\\\\=
4
.\end{array}
