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# 2^(4-1)^2/2^(3-2)

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Intern
Joined: 03 Oct 2010
Posts: 3

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Updated on: 10 Oct 2013, 04:05
4
2
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Difficulty:

15% (low)

Question Stats:

66% (00:21) correct 34% (00:25) wrong based on 447 sessions

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$$\frac{2^{(4-1)^2}}{2^{(3-2)}}=$$

A. 2^8
B. 2^7
C. 2^6
D. 2^5
E. 2^4

I'm overlooking something incredibly basic here. I know it. It's the first question I got on the GMAT prep math and I was shocked to see I got it WRONG. I've looked over it time and again, but can't find how to get the answer they are saying. They insist it's A, but I can take one look at that and see they are asking 2^6 over 2^2. Which would be 2^4. What am I missing?

Originally posted by Pollux on 07 Nov 2010, 12:21.
Last edited by Bunuel on 10 Oct 2013, 04:05, edited 1 time in total.
Edited the question.
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Joined: 02 Sep 2009
Posts: 49206
Re: I'm missing something basic here, but no idea what  [#permalink]

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07 Nov 2010, 13:11
2
1
Pollux wrote:
I'm overlooking something incredibly basic here. I know it. It's the first question I got on the GMAT prep math and I was shocked to see I got it WRONG. I've looked over it time and again, but can't find how to get the answer they are saying. They insist it's A, but I can take one look at that and see they are asking 2^6 over 2^2. Which would be 2^4. What am I missing?

2^(4-1)^2 over 2^(3-1)

A) 2^8
B) 2^7
C) 2^6
D) 2^5
E) 2^4

Writing mathematical symbols in posts: writing-mathematical-symbols-in-posts-72468.html

Also please check the questions when posting. Original question is $$\frac{2^{(4-1)^2}}{2^{(3-2)}}=?$$

If exponentiation is indicated by stacked symbols, the rule is to work from the top down, thus:
$$a^m^n=a^{(m^n)}$$ and not $$(a^m)^n$$, which on the other hand equals to $$a^{mn}$$.

So:
$$(a^m)^n=a^{mn}$$;

$$a^m^n=a^{(m^n)}$$ and not $$(a^m)^n$$.

According to above:

$$\frac{2^{(4-1)^2}}{2^{(3-2)}}=\frac{2^{3^2}}{2}=\frac{2^{(3^2)}}{2}=\frac{2^9}{2}=2^8$$.

For more check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.
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Re: I'm missing something basic here, but no idea what  [#permalink]

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07 Nov 2010, 13:25
Bunuel replied before I posted mine. It all makes sense now. Top down. Top down. Top down. Good to know!
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Re: Nested exponents - Gmatprep  [#permalink]

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05 Jan 2012, 05:48
Please differentiate between (a)^(b^c) and (a^b)^c

The first expression cannot be simplified further, i.e. you have to raise b to the power c to simplify, whereas the second expression can be simplified to a^bc.

Hope this makes it clear.
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23 Jul 2018, 23:06
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Re: 2^(4-1)^2/2^(3-2) &nbs [#permalink] 23 Jul 2018, 23:06
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