2019 AMC 10A Problem 1

Problem 1 of 25EasierAlgebra

What is the value of

2^{\left(0^{\left(1^9\right)}\right)}+\left(\left(2^0\right)^1\right)^9?

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Solution

We can evaluate from the top of each exponent tower downward:

\begin{aligned} &2^{\left(0^{\left(1^9\right)}\right)}\\ &\quad+\left(\left(2^0\right)^1\right)^9\\ &=2^{0^1}+(1^1)^9\\ &=2^0+1^9\\ &=2. \end{aligned}

Thus, C is the correct answer.

Concepts: exponent · order of operations

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