Difference between revisions of "2000 AMC 12 Problems/Problem 2"
Kevinmathz (talk | contribs) (→Solution) |
|||
(10 intermediate revisions by 9 users not shown) | |||
Line 2: | Line 2: | ||
== Problem == | == Problem == | ||
− | <math>2000(2000^{2000}) =</math> | + | <math>2000(2000^{2000}) = ?</math> |
+ | |||
+ | <math> \textbf{(A)} \ 2000^{2001} \qquad \textbf{(B)} \ 4000^{2000} \qquad \textbf{(C)} \ 2000^{4000} \qquad \textbf{(D)} \ 4,000,000^{2000} \qquad \textbf{(E)} \ 2000^{4,000,000} </math> | ||
− | |||
== Solution == | == Solution == | ||
− | <math> 2000(2000^{2000}) = (2000^{1})(2000^{2000}) = 2000^{2001} \Rightarrow \boxed{ | + | We can use an elementary exponents rule to solve our problem. |
+ | We know that <math>a^b\cdot a^c = a^{b+c}</math>. Hence, | ||
+ | <math> 2000(2000^{2000}) = (2000^{1})(2000^{2000}) = 2000^{2000+1} = 2000^{2001} \Rightarrow \boxed{\textbf{(A) } 2000^{2001}}</math> | ||
+ | |||
+ | Solution edited by armang32324 and integralarefun | ||
+ | |||
+ | == Solution 2== | ||
+ | |||
+ | We see that <math>a(a^{2000})=a^{2001}.</math> Only answer choice <math>\boxed{\textbf{(A)}}</math> satisfies this requirement. | ||
+ | |||
+ | -SirAppel | ||
+ | |||
+ | == Video Solution (Daily Dose of Math) == | ||
+ | |||
+ | https://www.youtube.com/watch?v=h0QtF9J0oPs | ||
+ | |||
+ | ~Thesmartgreekmathdude | ||
== See also == | == See also == |
Latest revision as of 16:24, 14 July 2024
- The following problem is from both the 2000 AMC 12 #2 and 2000 AMC 10 #2, so both problems redirect to this page.
Problem
Solution
We can use an elementary exponents rule to solve our problem.
We know that . Hence,
Solution edited by armang32324 and integralarefun
Solution 2
We see that Only answer choice
satisfies this requirement.
-SirAppel
Video Solution (Daily Dose of Math)
https://www.youtube.com/watch?v=h0QtF9J0oPs
~Thesmartgreekmathdude
See also
2000 AMC 12 (Problems • Answer Key • Resources) | |
Preceded by Problem 1 |
Followed by Problem 3 |
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 12 Problems and Solutions |
2000 AMC 10 (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.