Exponents Question with Solutions Last week I posted the laws of exponents that can be useful to know for standardized tests such as the ACT and SAT. You can see that post here: Laws of Exponents Here are the laws once again for your convenience. These should be memorized by students that are trying to get a perfect math score. I also mentioned that exponent problems can usually be solved by methods other than using the algebraic rules, but by using algebra you will solve them very, very quickly, giving you time to move on to other questions and to check your answers. Last week, I had this level 5 exponents problem for you to solve: Level 5 Exponents Question If y = 7x, then which of the following expressions is equivalent to 49x − 7x+2 for all positive integer values of x? A) y² B) y² − y C) y² − 7y D) y² − 49y Let’s look at two different ways to solve this problem. Algebraic Solution Let’s solve this algebraically using the exponent laws. 49x – 7x+2= (7²)x −7x72 = (7x)² − 49(7x) = y² – 49y In the first equality we rewrote 49 as 7² and used the third law in our list to rewrite 7x+2 as 7x7². In the second equality we simply rewrote 7² as 49. Finally, in the third equality we replaced 7x by y twice. This is choice D. Solution by Picking Numbers And here is an alternative solution using the strategy of “picking numbers”. Let’s choose a value for x, say x = 2. Then we have: y = 7² = 49, and 49x − 7x+2 = 49² − 74 = 0. Put a nice, big, dark circle around 0. Make it obvious that this is the value you are expecting to be your solution. Now substitute y = 49 into each answer choice: A) y² = 49² = 2401 B) y² − y = 49² − 49 = 2401 – 49 = 2352 C) y² − 7y = 49² – 7*49 = 2401 – 343 = 2058 D) y² − 49y = 49² – 49*49 = 2401 – 2401 = 0 Since A, B, and C are incorrect, we can eliminate them. Therefore the answer choice is D. As you can see the method of picking numbers is more time consuming than the algebraic method, but you will get the right answer as long as you are careful. Whichever method you choose, you should try to check your answer with a different method if possible. If you can only solve the problem by picking numbers, then at least pick different numbers when you are “checking.” And don’t forget to check out the Get 800 collection of test prep books. If you liked this article, please share it with your Facebook friends: Comments comments