Exponents and Roots : GMAT Problem Solving (PS)
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# Exponents and Roots

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28 Oct 2011, 02:35
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Simplify the following fraction:

2^21/4^4(4^5-4^3)
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28 Oct 2011, 04:12
answer is supposed to be: 2^7/15?!
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28 Oct 2011, 09:55
Can anybody explain the way of calculation? That would be really great!
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28 Oct 2011, 15:27
Hi Corinna,

Here is my working out.

First, let's simplify the bottom expression.

4^4 (4^5 -4^3)

Expand

4^9 - 4^7

Take out common factor

4^7 (4^2 - 1)

= 4^7 (15)

Turn the 4 into a base of 2, which is 2^2

So (2^2)^7 ( 15)

= 2^14 (15)

Now we can cancel out the 2^14 by the 2^21 on the top so the top becomes 2^7

2^7/15

I hope that makes sense.
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28 Oct 2011, 17:28
This question is a bit silly without answer choices as it's not clear when the simplification is finished, but anyways:

$$\frac{2^{21}}{4^4*(4^5-4^3)}$$

$$\frac{2^{21}}{2^8*(2^{10}-2^6)}$$

$$\frac{2^{21}}{2^{14}*(2^4-1)}$$

$$\frac{2^{7}}{2^4-1}$$

$$\frac{2^{7}}{15}$$

$$\frac{128}{15}$$
Re: Exponents and Roots   [#permalink] 28 Oct 2011, 17:28
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