((12^2+5^2)^1/2)^3
You asked:
Evaluate the expression: \({\left( \frac{{\left( {12}^{2} + {5}^{2} \right)}^{1}}{2} \right)}^{3}\)
MathBot Answer:
\[{\left( \frac{{\left( {12}^{2} + {5}^{2} \right)}^{1}}{2} \right)}^{3} = \frac{4826809}{8} = 603351.125\]
\[\begin{aligned}{\left( \frac{{\left( {12}^{2} + {5}^{2} \right)}^{1}}{2} \right)}^{3}& = \left(\left(12^{2} + 5^{2}\right)^{1} \cdot \frac{1}{2}\right)^{3}\\& = \left(\left(144 + 5^{2}\right)^{1} \cdot \frac{1}{2}\right)^{3}\\& = \left(\left(144 + 25\right)^{1} \cdot \frac{1}{2}\right)^{3}\\& = \left(169^{1} \cdot \frac{1}{2}\right)^{3}\\& = \left(\frac{169}{2}\right)^{3}\\& = \frac{4826809}{8}\end{aligned}\]