(2^-2+2^-3)^-1
You asked:
Evaluate the expression: \({\left( {2}^{-2} + {2}^{-3} \right)}^{-1}\)
MathBot Answer:
\[{\left( {2}^{-2} + {2}^{-3} \right)}^{-1} = \frac{8}{3} = 2.\overline{6}\]
\[\begin{aligned}{\left( {2}^{-2} + {2}^{-3} \right)}^{-1}& = \frac{1}{\frac{1}{2^{2}} + \frac{1}{2^{3}}}\\& = \frac{1}{\frac{1}{4} + \frac{1}{2^{3}}}\\& = \frac{1}{\frac{1}{4} + \frac{1}{8}}\\& = \frac{1}{\frac{3}{8}}\\& = \frac{8}{3}\end{aligned}\]