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

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Senior Manager
Joined: 08 Nov 2010
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10 Dec 2010, 11:01
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Difficulty:

5% (low)

Question Stats:

67% (00:16) correct 33% (00:14) wrong based on 380 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

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Posts: 46129
Re: Powers. question number 1... [#permalink]

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10 Dec 2010, 11:06
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2
$$\frac{2^{(4-1)^2}}{2^{(3-2)}}=?$$

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: Powers. question number 1... [#permalink]

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10 Dec 2010, 11:13
2
Roger, thanks. so simple... damn.
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Updated on: 05 Jan 2012, 04:45
Dont we just multiply nested exponents?
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Originally posted by BrainFog on 05 Jan 2012, 02:44.
Last edited by BrainFog on 05 Jan 2012, 04:45, edited 1 time in total.
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Re: Nested exponents - Gmatprep [#permalink]

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05 Jan 2012, 03:33
1
The answer is 2^9/2 = 2^8

Option (A)

Remember that 2^(4-1)^2 = 2^9. Dividing by 2 in the denominator, you get 2^(9-1) = 2^8, which is the answer.
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Updated on: 11 Mar 2015, 03:02
- Edited -
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Originally posted by BrainFog on 05 Jan 2012, 04:47.
Last edited by BrainFog on 11 Mar 2015, 03:02, edited 1 time in total.
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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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Re: Nested exponents - Gmatprep [#permalink]

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05 Jan 2012, 06:09
This is x^y^z.
y^z will have to be solved first because of PEMDAS and parentheses will have to be removed.
y^z is (4-1)^2=3^2=9=2^9/2=2^8
Hence A.
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Re: Nested exponents - Gmatprep [#permalink]

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05 Jan 2012, 15:25
2^(4-1)^2 = 2^3^2 = 2^9
2^(3-2) = 2^1

Therefore, we get 2^9/2^1 = 2^(9-1) = 2^8 -> A
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13 Mar 2012, 11:02
http://i39.tinypic.com/dcyps1.png

How the hell did I get this wrong? I still don't believe the correct answer.

A) 2^8
B) 2^7
C) 2^6
D) 2^5
E) 2^4
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13 Mar 2012, 12:19
1

hope it help's
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10 Sep 2013, 06:25
Bumping for review and further discussion.
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17 May 2017, 09:57
Great question, its so easy to pick 2^6. But the actual answer is 2^8. Simple mistake can be very costly on test day. Thank you for your explanation.
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Re: (2^(4-1)^2)/(2^(3-2))   [#permalink] 17 May 2017, 09:57
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