What is the value of 2^(0^(1^9))+((2^0)^1)^9?

2019 AMC 10A Problem 1 — Solution

2019 AMC 10A Problem 1

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What is the value of $2^{\left(0^{\left(1^9\right)}\right)}+\left(\left(2^0\right)^1\right)^9?$

$0$

$1$

$2$

$3$

$4$

Answer: C

Concepts:exponent order of operations

Difficulty rating: 560

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.

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