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Competency in Focus: Powers of Numbers This problem from American Mathematics contest (AMC 8, 2013) is based on basic algebra and Powers of Numbers.
First look at the knowledge graph.
Next understand the problem
If , , and , what is the product of , , and ?
Source of the problem
American Mathematical Contest 2013, AMC 8 Problem 15
Basic algebra and Powers of Numbers
Challenges and Thrills in Pre College Mathematics Excursion Of Mathematics
Start with hints
Do you really need a hint? Try it first!
First, we’re going to solve for . Start with . Then, change to . Subtract from both sides to get .Now we can write 9 as \(3^2\) .So, from here we can say that p=2.
Now, solve for . Since , must equal , and 32 can be written as \( 2^5 \) .So from here we have r=5.
Similarly now, solve for . can be simplified to which simplifies further to =\(6^4\) , which gives s=4.
Lastly, equals which equals . So, the answer is 40.
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