Answer
$\dfrac{16}{25}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the laws of exponents to simplify the given expression, $
\left( -\dfrac{5}{4} \right)^{-2}
.$
$\bf{\text{Solution Details:}}$
Since $\left( \dfrac{x}{y} \right)^m=\dfrac{x^m}{y^m},$ then the expression above is equivalent to
\begin{array}{l}\require{cancel}
\left( \dfrac{-5}{4} \right)^{-2}
\\\\=
\dfrac{(-5)^{-2}}{4^{-2}}
.\end{array}
Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{4^{2}}{(-5)^{2}}
\\\\=
\dfrac{16}{25}
.\end{array}
