Answer
$-\dfrac{37}{20}$
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, $
\left(-\dfrac{2^3}{5}-\dfrac{3}{4}\right)-\left(-\dfrac{1}{2}\right)
.$
$\bf{\text{Solution Details:}}$
Simplifying the exponents the entire expression above becomes
\begin{array}{l}\require{cancel}
\left(-\dfrac{8}{5}-\dfrac{3}{4}\right)-\left(-\dfrac{1}{2}\right)
.\end{array}
Simplifying the parenthesis by making the fractions similar, the expression above becomes
\begin{array}{l}\require{cancel}
\left(-\dfrac{8}{5}\cdot\dfrac{4}{4}-\dfrac{3}{4}\cdot\dfrac{5}{5}\right)-\left(-\dfrac{1}{2}\right)
\\\\=
\left(-\dfrac{32}{20}-\dfrac{15}{20}\right)-\left(-\dfrac{1}{2}\right)
\\\\=
\left(\dfrac{-32-15}{20}\right)-\left(-\dfrac{1}{2}\right)
\\\\=
\dfrac{-47}{20}-\left(-\dfrac{1}{2}\right)
.\end{array}
Simplifying the product/quotient, the expression above becomes
\begin{array}{l}\require{cancel}
\dfrac{-47}{20}+\dfrac{1}{2}
.\end{array}
Simplifying the sum/difference by making the fractions similar, the expression above becomes
\begin{array}{l}\require{cancel}
\dfrac{-47}{20}+\dfrac{1}{2}\cdot\dfrac{10}{10}
\\\\=
\dfrac{-47}{20}+\dfrac{10}{20}
\\\\=
\dfrac{-47+10}{20}
\\\\=
\dfrac{-37}{20}
\\\\=
-\dfrac{37}{20}
.\end{array}
