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# M07-32

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Math Expert
Joined: 02 Sep 2009
Posts: 47946

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16 Sep 2014, 00:35
1
1
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:58) correct 24% (00:55) wrong based on 67 sessions

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$$(\frac{1}{2})^2 + (\frac{1}{4})^{-2} + (\frac{1}{8})^{\frac{2}{3}} + (\frac{1}{4})^{\frac{1}{2}} =$$ ?

A. $$20(\frac{3}{4})$$
B. $$17$$
C. $$9(\frac{1}{2})$$
D. $$6$$
E. $$4(\frac{3}{4})$$

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Math Expert
Joined: 02 Sep 2009
Posts: 47946

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16 Sep 2014, 00:36
Official Solution:

$$(\frac{1}{2})^2 + (\frac{1}{4})^{-2} + (\frac{1}{8})^{\frac{2}{3}} + (\frac{1}{4})^{\frac{1}{2}} =$$ ?

A. $$20(\frac{3}{4})$$
B. $$17$$
C. $$9(\frac{1}{2})$$
D. $$6$$
E. $$4(\frac{3}{4})$$

Simplify the expression as follows.
$$\frac{1}{2^2} = \frac{1}{4}$$
$$(\frac{1}{4})^{-2} = 4^2 = 16$$

A number taken to a negative power equals its reciprocal taken to the same power but with a positive sign.
$$\frac{1}{8^{\frac{2}{3}}} = \frac{1}{\sqrt[3]{8^2}} = \frac{1}{4}$$

As a general rule,
$$(\frac{a}{b})^{\frac{n}{m}} = \sqrt{(\frac{a}{b})^n}$$
$$\frac{1}{4}^{\frac{1}{2}} = \frac{1}{2}$$

The sum is:
$$\frac{1}{4} + 16 + \frac{1}{4} + \frac{1}{2} = 17$$

_________________
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Joined: 03 Aug 2015
Posts: 56
Concentration: Strategy, Technology
Schools: ISB '18, SPJ GMBA '17
GMAT 1: 680 Q48 V35

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28 Dec 2015, 23:21
Bunuel wrote:
Official Solution:

$$(\frac{1}{2})^2 + (\frac{1}{4})^{-2} + (\frac{1}{8})^{\frac{2}{3}} + (\frac{1}{4})^{\frac{1}{2}} =$$ ?

A. $$20(\frac{3}{4})$$
B. $$17$$
C. $$9(\frac{1}{2})$$
D. $$6$$
E. $$4(\frac{3}{4})$$

Simplify the expression as follows.
$$\frac{1}{2^2} = \frac{1}{4}$$
$$(\frac{1}{4})^{-2} = 4^2 = 16$$

A number taken to a negative power equals its reciprocal taken to the same power but with a positive sign.
$$\frac{1}{8^{\frac{2}{3}}} = \frac{1}{\sqrt[3]{8^2}} = \frac{1}{4}$$

As a general rule,
$$(\frac{a}{b})^{\frac{n}{m}} = \sqrt{(\frac{a}{b})^n}$$
$$\frac{1}{4}^{\frac{1}{2}} = \frac{1}{2}$$

The sum is:
$$\frac{1}{4} + 16 + \frac{1}{4} + \frac{1}{2} = 17$$

Hello Bunuel,

If i am not wrong, you have assumed as m=2 at this case.

Pls clarify..................

And also if you could share some similar question for practice, it would be great 8-)

Thanks,
Arun
Intern
Joined: 08 Jul 2017
Posts: 3

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25 Sep 2017, 08:40
Hi Bunuel, I have the same doubt as ArunpriyanJ

Appreciate if you can explain a bit further why we assume m=2 in your explanation.

Thanks!
Re: M07-32 &nbs [#permalink] 25 Sep 2017, 08:40
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# M07-32

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