## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$4$
$\bf{\text{Solution Outline:}}$ 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}