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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
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?
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07 Nov 2010, 13:11
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Pollux
\(\frac{2^{(4-1)^2}}{2^{(3-2)}}=\)
A. 2^8
B. 2^7
C. 2^6
D. 2^5
E. 2^4
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 the above:
\(\frac{2^{(4-1)^2}}{2^{(3-2)}}=\frac{2^{3^2}}{2}=\frac{2^{(3^2)}}{2}=\frac{2^9}{2}=2^8\).
Answer: A.
For more check Number Theory chapter of Math Book: https://gmatclub.com/forum/math-number-theory-88376.html
Hope it helps.
General Discussion
05 Jan 2012, 05:48
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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.
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.
