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2014 AMC 10B Problem 2

Problem 2 of 25EasierAlgebra

What is 23+232−3+2−3?\dfrac{2^3 + 2^3}{2^{-3} + 2^{-3}}?

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Solution

23+232−3+2−3=2⋅232⋅2−3=26=64\begin{aligned} \dfrac{2^3 + 2^3}{2^{-3} + 2^{-3}} &= \dfrac{2\cdot 2^3}{2\cdot 2^{-3}} \\&=2^6 \\&= 64 \end{aligned} Thus, the correct answer is E .

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Concepts: exponent

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.