$\frac{ 9 }{ 16 }-{\left( 1 \frac{ 1 }{ 2 } \right)}^{3}$
Convert the mixed number to an improper fraction$\frac{ 9 }{ 16 }-{\left( \frac{ 3 }{ 2 } \right)}^{3}$
To raise a fraction to a power, raise the numerator and denominator to that power$\frac{ 9 }{ 16 }-\frac{ 27 }{ 8 }$
Subtract the fractions$\begin{align*}&-\frac{ 45 }{ 16 } \\&\begin{array} { l }-2 \frac{ 13 }{ 16 },& -2.8125\end{array}\end{align*}$