Evaluate: ((3)/(4))^2-(1 (1)/(2))^3

Expression: ${\left( \frac{ 3 }{ 4 } \right)}^{2}-{\left( 1 \frac{ 1 }{ 2 } \right)}^{3}$

To raise a fraction to a power, raise the numerator and denominator to that power

$\frac{ 9 }{ 16 }-{\left( 1 \frac{ 1 }{ 2 } \right)}^{3}$

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

$\begin{align*}&-\frac{ 45 }{ 16 } \\&\begin{array} { l }-2 \frac{ 13 }{ 16 },& -2.8125\end{array}\end{align*}$