Answer
$-\dfrac{12}{5}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the order of operations (PEMDAS - Parenthesis/Exponents, Multiplication/Division, Addition/Subtraction) to simplify the given expression, $
\dfrac{6(-4)-3^2(-2)^3}{-5[-2-(-6)]}
.$
$\bf{\text{Solution Details:}}$
Simplifying the exponents, the expression above becomes
\begin{array}{l}\require{cancel}
\dfrac{6(-4)-9(-8)}{-5[-2-(-6)]}
.\end{array}
Simplifying the parenthesis, the expression above becomes
\begin{array}{l}\require{cancel}
\dfrac{6(-4)-9(-8)}{-5[-2+6]}
\\\\=
\dfrac{6(-4)-9(-8)}{-5[4]}
.\end{array}
Simplifying the product/quotient, the expression above becomes
\begin{array}{l}\require{cancel}
\dfrac{-24+72}{-20}
.\end{array}
Simplifying the sum/difference by making the fractions similar, the expression above becomes
\begin{array}{l}\require{cancel}
\dfrac{48}{-20}
\\\\=
\dfrac{\cancel4(12)}{\cancel4(-5)}
\\\\=
\dfrac{12}{-5}
\\\\=
-\dfrac{12}{5}
.\end{array}
