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GRE Math Video Lessons: Exponents

Exponents are troublesome; fortunately, they do not need to be. What I plan to do in this series is show you the basics, so that you can move confidently through the intermediate level, and even the advanced level.

I’ve created three lessons, corresponding to basic, medium, and advanced. You can watch them here:

Exponents Level 1

Exponents Level 2

Exponents Level 3

Once you have a sense of how the fundamentals of exponents work for each level, you can test yourself with a GRE problem. After all, knowing only the fundamentals does not mean you will answer a GRE question correctly.

Remember, the GRE is testing the way you think. That means the GRE will try to throw you off balance by presenting an exponents question that, at first glance, will give you pause. They expect you to be able to find an effective approach to the problem. Only then can you apply the fundamentals you’ve learned. In essence, the GRE is wrapping up a problem; unraveling a problem, so to speak, is half the battle.

 

Level 1

4^2=4*4

4^3=4*4*4

4^2*4^3=4^5

(4^3)^2=4^6

2^2=4

4^6=(2^2)^6=2^12

{2^5}/{2^3}=2^2=4

{2^3}/{2^5}=1/4

 

So now, I am going to take the fundamentals covered above, and I am going to wrap them up in a GRE problem. See if you can unravel the question below.

Practice Problem:

If (4^2)^3*2^6=2^y, what is the value of y?

(A)  6

(B)  12

(C)  18

(D) 36

(E)  72

 

Answer: C

If you are even a bit unsure about any of the above, you will definitely want to watch the video.

 

Level 2

It’s going to be a little more difficult here, but if you are confident with level one, give Level 2 a try:

4^{1/2} = 2

8^{2/3} = 4

 

4^{-2}=1/16

3^{-3}=1/27

 

4^{-1/2}= 1/{4^{1/2}}=1/2

27^{-2/3} = {1/27}^{2/3} = 1/9

 

Once again, I am going to take the fundamentals you’ve learned this far and I am going to turn them into a GRE problem:

 

3^{-n}*3^{-n} = 1/81, what is the value of n?

(A)   -2

(B)   0

(C)   1

(D)   2

(E)   4

 

Answer: D

If you were unable to answer the problem correctly, or if any of the above did not make sense, take a look at the video.

 

Level 3

Congratulations! You’ve already learned enough to answer most GRE exponent problems. In this level, you are going to learn more advanced techniques, perfect for those students looking to score above the top 85%.

5^10 + 5^9 + 5^8 = 5^8 (5^2 + 5^1 + 1) = 5^8 (31)

 

{5^17 + 5^16 + 5^15}/{5^14(31)} = {5^15 (5^2 + 5 + 1)}/{5^14 (31)} = {5(31)}/31 = 5

{5^24*4^12}/{10^24} = 1

 

Practice Problem:

If n ={2^{-10}+2^{-9}}/{(7^{-1}) (5^9)} then n is a terminating decimal with how many zeroes after the decimal point before the first non-zero digit?

(A)  2

(B)  3

(C)  5

(D)  7

(E)  9

 

Answer (D). This question is about as difficult as any exponent problem you will see on the GRE. So, if you got it right, good job! If you are unsure about the solution to the problem, you can see the steps in the picture below (scroll down):

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If you would like more practice on exponents, check out the Official Guide problems (there are a few exponent problems in the book). And, if you encounter any obstacles, don’t despair—I’ve recorded video explanations for every single problem in the Official Guide. For even more practice on exponents, and video explanations, give Magoosh a try.

Magoosh students score 12 points better than average on the GRE. Click here to  learn more!

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