(1/3)^-2+(1/4)^-2+(1/2)^-2

asked by guest
on Nov 25, 2024 at 5:33 am



You asked:

Evaluate the expression: \({\left( \frac{1}{3} \right)}^{-2} + {\left( \frac{1}{4} \right)}^{-2} + {\left( \frac{1}{2} \right)}^{-2}\)

MathBot Answer:

\[{\left( \frac{1}{3} \right)}^{-2} + {\left( \frac{1}{4} \right)}^{-2} + {\left( \frac{1}{2} \right)}^{-2} = 29\]

\[\begin{aligned}{\left( \frac{1}{3} \right)}^{-2} + {\left( \frac{1}{4} \right)}^{-2} + {\left( \frac{1}{2} \right)}^{-2}& = \frac{1}{(\frac{1}{3})^{2}} + \frac{1}{(\frac{1}{4})^{2}} + \frac{1}{(\frac{1}{2})^{2}}\\& = 9 + \frac{1}{(\frac{1}{4})^{2}} + \frac{1}{(\frac{1}{2})^{2}}\\& = 9 + 16 + \frac{1}{(\frac{1}{2})^{2}}\\& = 9 + 16 + 4\\& = 25 + 4\\& = 29\end{aligned}\]

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