Difference between revisions of "2019 AMC 10A Problems/Problem 1"

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==Problem 1==
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== Problem ==
 
What is the value of <cmath>2^{\left(0^{\left(1^9\right)}\right)}+\left(\left(2^0\right)^1\right)^9?</cmath>
 
What is the value of <cmath>2^{\left(0^{\left(1^9\right)}\right)}+\left(\left(2^0\right)^1\right)^9?</cmath>
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<math>\textbf{(A) } 0 \qquad\textbf{(B) } 1 \qquad\textbf{(C) } 2 \qquad\textbf{(D) } 3 \qquad\textbf{(E) } 4</math>
 
<math>\textbf{(A) } 0 \qquad\textbf{(B) } 1 \qquad\textbf{(C) } 2 \qquad\textbf{(D) } 3 \qquad\textbf{(E) } 4</math>
  
==Solution==
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== Solution ==  
The first part can be rewritten as <cmath>2^{0^{1}}=2^{0}=1.</cmath>
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<math>2^{\left(0^{\left(1^9\right)}\right)}+\left(\left(2^0\right)^1\right)^9</math>
The second part is <cmath>(1^{1})^{9}=1^{9}=1.</cmath>
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Adding these up gives <math>\boxed{\textbf{(C) }2}.</math>
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<math>1+1 = \boxed{2}</math> which corresponds to <math>\boxed{\text{C}}</math>.
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== Video Solution 1 ==
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https://youtu.be/K8je0WYBHFc
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Education, The Study Of Everything
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== Video Solution 2==
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https://youtu.be/Ad8WKcwZcTA
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~savannahsolver
  
 
== See Also ==
 
== See Also ==
 
 
{{AMC10 box|year=2019|ab=A|before=First Problem|num-a=2}}
 
{{AMC10 box|year=2019|ab=A|before=First Problem|num-a=2}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 19:30, 20 November 2020

Problem

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

$\textbf{(A) } 0 \qquad\textbf{(B) } 1 \qquad\textbf{(C) } 2 \qquad\textbf{(D) } 3 \qquad\textbf{(E) } 4$

Solution

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

$=  1+1 = \boxed{2}$ which corresponds to $\boxed{\text{C}}$.

Video Solution 1

https://youtu.be/K8je0WYBHFc

Education, The Study Of Everything


Video Solution 2

https://youtu.be/Ad8WKcwZcTA

~savannahsolver

See Also

2019 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions

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