GMAT Ninja Quant Ep 4: Exponents

Do you struggle with exponents questions on the GMAT or Executive Assessment? Do you get baffled when it comes to negative or fractional exponents? Do you know when and how to convert the "base" in a GMAT exponents question?

In this video, John Michael -- a GMAT Ninja tutor -- will show you how to think about GMAT exponents questions efficiently and effectively. He'll help you understand how a flexible, consistent approach to exponents can increase your efficiency and accuracy.

This video will cover:
➡️ Base conversion
➡️ Factoring exponents
➡️ Negative and fractional exponents

This video is for you if:
➡️ You don’t know where to start on exponent problems
➡️ You “know” all the rules but still struggle
➡️ You lack efficiency or flexibility in applying exponent rules

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Chapters:
00:00 Introduction
01:46 Q1 - Exponents Basics
09:22 Q2 - Fractions and Negative Powers
19:51 Q3 - Factoring Exponents
27:47 Q4 - Factoring Exponents Part II
37:19 Q5 - Hidden Roots
45:41 Q6 - Scientific Notation and Hidden Quadratics

[xanderark]

My mind was exhausted after solving q5 and 48:19 made me smile a little, love your teaching Mr. John

[theEtch]

I did Q4 by substitution (although it took me 10 minutes). If the possible answers that a and b can fit into are 3, 4, 5, 6 and 7 then the only answers for a and b are 1-6. Assume it can't be negative as that would leave us with a fraction which would just be too complicated. The values that add up to 3 are 1 and 2, so when we've calculated for the a side we don't need to calculate again for the values adding up to 4, as we know a=1, b=1, a=2, b=2, so just need to calculate b=3, as we can assume b>a since you'd need more powers of 2 to catch up with powers of 5. With a=3 we get 125-5 =120 which isn't enough for 75x2^any positive integer. So among the possible values of a, a must be 4, so you just solve or substitute for b which must be 3. With a=4, 5^5 - 5^(4-2) = 625 - 5^2 = 600. as 75*2(^3) = 75*8 =600.
600 = 75*2^b
600/75 = 8 (easily calculable with 75*2 =150, 4*150=600.
8 is 2 cubed.
a=4, b=3
answer is E, 7.

(I know this is the most inefficient way possible but it might help some people)

[arbaazkhan]

Thank you for this session, that is some excellent content!

I had another approach for Q5 and Q6. Please let me know if they are right or if there is any underlying flaw.

For Q5, instead of solving the given equation, I tried to put that value in the question after manipulating it a bit.
Question => 5^(4x-2) = (5^4x)/5^2. Let this be A, then A^2 = (5^8x)/5^4 = 62500/625 = 100. That gives me A as 10.

For Q6, instead of solving both the parts, here is what I did.
1st Part = Approximate it to 3 (Remember this value is higher than the actual value since we have decreased the denominator and increased the numerator)
2nd Part = The numerator is exactly divisible here by the denominator (Hint : See 5 at the end so just start dividing by 5). After division, it gives 2.005

Now, 1st part - 2nd part = 3 - 2.005 = 0.995
Note : Since 3 was higher than the actual value, the subtracted value (0.995) is also higher than the actual value which means the actual value has to be smaller than 0.995 and the only option for that is A (0.994). So, option A is correct.

Please feel free to reply in case of any questions.

[HieuNguyen]

the last one was difficult bloody hell

[kaws]

Appreciate for your explanation, John!

[bigdong]

great video but honestly im completly cooked in quant

[jamesgraf]

Loved the video.

For q6 should the equation of reduce to 1/1, 000, 000 and not 1/100, 000 or am I missing an principle here?
1/100, 000 would be 10^-5 correct?

[marcopg]

Loving all the content. Im starting to get the feeling the Gmat has a compendium of traps and tricks for Quant and the only way to ace, it is to have encountered and learned them all beforehand. There is no way I could have answered any question beyond 1 & 2, under two mins when encountering them for the first time. Will I get a sense of this whole "compendium" from all the videos on the channel ?

[LastWayLp]

Honestly great video. At the start you always say if you lack some mathematical basics learn these first, can you recommend some material here? (I find it hard to finde specific math material related to gmat (no calculater usuable etc.) My exam is in 2 weeks, I was sufficient in VR and DS in the mock exam but I roughly need 70th percentile in Quant for my needed score and will all solutions make sense, 2mins seem very hard for me, especially with questions like the last one 😅

[LittleMsSunshineXox]

How do I solve this in 2 Min? Either way I love these videos! <3

[NoamVaizel]

Just to get a perspective, on a scale of 1-10, where 10 is a 99th percentage level Q, what
If the difficulty of the last Q?

[vikaskumarsinha]

For Q6, is there a pattern? If the denominator is a factor of the numerator, like a2 - b2 divided by a - b (or a+b), does the result simplify to the difference between the denominators? I'm trying to find a shortcut since solving it properly in 3 minutes is difficult and prone to silly mistakes (at least for me)

Your way of teaching is just awesome, thanks for the great work :)

[natajojishvili]

Thank you, first of all, for your videos! In the last question (Q6), it seems there is a small mechanical error - the fraction should have 1, 000, 000 instead of 100, 000. The solution itself is correct (10^6), but the number shown in the fraction appears to be incorrect.

[duncanoboyle]

On question 4 I always struggle to understand factoring when the cursed letters are thrown into the mix. In the piece of the equation 5^a - 5^a-2, are you essentially saying 5^a-2 when a=2, 5^0 is 1, so I am left with a=2, 5^2, factored out being 5^a-2 (5^2 -1)?

[ashujoodha]

Are those examples also applicable to EA? or they are not that difficult?

[hofstage]

why isn’t the second to last question 20? you get 5^8x = 5^6 * 2^2; x = 6/8; then plug into second equation which gets 5^3-2 =1, so final answer is 5* 2^2 =20

[ghostsvoice]

are questions this easy in actual test also ? ( Except last one )