# What are we learning ?

**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

##### Key Competency

Basic algebra and Powers of Numbers

##### Difficulty Level

4/10

##### Suggested Book

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.

# Connected Program at Cheenta

#### Amc 8 Master class

Cheenta AMC Training Camp consists of live group and one on one classes, 24/7 doubt clearing and continuous problem solving streams.