Calculate: (1-(2)/(3))^{-2}-\sqrt[3]{1-(7)/(8)}-(-(1)/(2)+(1)/(3))^{-1}

Expression: ${\left( 1-\frac{ 2 }{ 3 } \right)}^{-2}-\sqrt[3]{1-\frac{ 7 }{ 8 }}-{\left( -\frac{ 1 }{ 2 }+\frac{ 1 }{ 3 } \right)}^{-1}$

Calculate the difference

${\left( \frac{ 1 }{ 3 } \right)}^{-2}-\sqrt[3]{1-\frac{ 7 }{ 8 }}-{\left( -\frac{ 1 }{ 2 }+\frac{ 1 }{ 3 } \right)}^{-1}$

Calculate the sum

${\left( \frac{ 1 }{ 3 } \right)}^{-2}-\sqrt[3]{1-\frac{ 7 }{ 8 }}-{\left( -\frac{ 1 }{ 6 } \right)}^{-1}$

Express with a positive exponent using ${\left( \frac{ 1 }{ a } \right)}^{-n}={a}^{n}$

${3}^{2}-\sqrt[3]{1-\frac{ 7 }{ 8 }}-{\left( -\frac{ 1 }{ 6 } \right)}^{-1}$

Any expression raised to the power of $-1$ equals its reciprocal

${3}^{2}-\sqrt[3]{1-\frac{ 7 }{ 8 }}-\left( -6 \right)$

Evaluate the power

$9-\sqrt[3]{1-\frac{ 7 }{ 8 }}-\left( -6 \right)$

When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses

$9-\sqrt[3]{1-\frac{ 7 }{ 8 }}+6$

Add the numbers

$15-\sqrt[3]{1-\frac{ 7 }{ 8 }}$

Calculate the difference

$15-\sqrt[3]{\frac{ 1 }{ 8 }}$

Evaluate the cube root

$15-\frac{ 1 }{ 2 }$

Calculate the difference

$\begin{align*}&\frac{ 29 }{ 2 } \\&\begin{array} { l }14 \frac{ 1 }{ 2 },& 14.5\end{array}\end{align*}$