(1/36)^-2/3 + (1/279)^-2/4
You asked:
Evaluate the expression: \(\frac{{\left( \frac{1}{36} \right)}^{-2}}{3} + \frac{{\left( \frac{1}{279} \right)}^{-2}}{4}\)
MathBot Answer:
\[\frac{{\left( \frac{1}{36} \right)}^{-2}}{3} + \frac{{\left( \frac{1}{279} \right)}^{-2}}{4} = \frac{79569}{4} = 19892.25\]
\[\begin{aligned}\frac{{\left( \frac{1}{36} \right)}^{-2}}{3} + \frac{{\left( \frac{1}{279} \right)}^{-2}}{4}& = \frac{1}{(\frac{1}{36})^{2}} \cdot \frac{1}{3} + \frac{1}{(\frac{1}{279})^{2}} \cdot \frac{1}{4}\\& = \frac{1296}{3} + \frac{1}{(\frac{1}{279})^{2}} \cdot \frac{1}{4}\\& = 432 + \frac{1}{(\frac{1}{279})^{2}} \cdot \frac{1}{4}\\& = 432 + \frac{77841}{4}\\& = \frac{79569}{4}\end{aligned}\]