Which of the following equivalent to (1/8)^4?

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

Which of the following equivalent to (1/8)^4?

by AAPL » Sun Nov 26, 2017 9:01 am

Which of the following equivalent to (1/8)^4?

$$\left(A\right)\ \left(0.5\right)^5$$
$$\left(B\right)\ \left(0.25\right)^3$$
$$\left(C\right)\ \left(0.25\right)^6$$
$$\left(D\right)\ \left(0.4\right)^3$$
$$\left(E\right)\ \left(0.8\right)^2$$

The OA is C.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

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Source: Beat The GMAT — Problem Solving | Sun Nov 26, 2017 9:01 am

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by [email protected] » Sun Nov 26, 2017 9:54 am

Hi AAPL,

Certain Quant questions are made easier if you 'convert' the given information from one format to another. Here, we're given answer choices as decimals, but you would likely find this question far easier to deal with if you converted those decimals to fractions. In addition - while it's not necessary - you might also find it helpful to use prime factorization on the prompt.

We're asked to find the equivalent of (1/8)^4. That's the equivalent of...
(1)/([2^3]^4) =
1/(2^12)

Thus, we're looking for an answer that involves a '2' raised to the 12th power. As such, the correct answer will likely be either Answer B or C (as .25 = 1/4 and 1/4 = 1/2^2).

With (.25)^6, we have...
(1/4)^6 =
1/[2^2]^6 =
1/(2^12)
This is an exact match for what we were looking for, so this must be the answer.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

Which of the following equivalent to (1/8)^4?

by EconomistGMATTutor » Tue Nov 28, 2017 5:30 am

Which of the following equivalent to (1/8)^4?

$$\left(A\right)\ \left(0.5\right)^5$$
$$\left(B\right)\ \left(0.25\right)^3$$
$$\left(C\right)\ \left(0.25\right)^6$$
$$\left(D\right)\ \left(0.4\right)^3$$
$$\left(E\right)\ \left(0.8\right)^2$$

The OA is C.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

Hi AAPL,
Let's take a look at your question.

We will first write the given expression in its simplest form.
$$\left(\frac{1}{8}\right)^{^4}=\left(\frac{1}{2\times2\times2}\right)^{^4}$$
$$ =\left(\frac{1}{2^3}\right)^{^4}=\left(\frac{1}{2}\right)^{^{12}}$$

Now we will check which of the given options is equivalent to the expression above.

OPTION A:
$$\left(0.5\right)^{^5}$$
$$=\left(\frac{5}{10}\right)^{^5}=\left(\frac{1}{2}\right)^{^5}\ne\left(\frac{1}{2}\right)^{^{12}}$$

OPTION B:
$$\left(0.25\right)^{^3}$$
$$=\left(\frac{25}{100}\right)^{^3}=\left(\frac{1}{4}\right)^{^3}=\left(\frac{1}{2^2}\right)^{^3}=\left(\frac{1}{2}\right)^{^6}\ne\left(\frac{1}{2}\right)^{^{12}}$$

OPTION C:
$$\left(0.25\right)^{^6}$$
$$=\left(\frac{25}{100}\right)^{^6}=\left(\frac{1}{4}\right)^{^6}=\left(\frac{1}{2^2}\right)^{^6}=\left(\frac{1}{2}\right)^{^{12}}$$

Therefore, Option C is correct.

Hope it helps.
I am available if you'd like any follow up.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sat Oct 05, 2019 3:41 pm

AAPL wrote:Which of the following equivalent to (1/8)^4?

$$\left(A\right)\ \left(0.5\right)^5$$
$$\left(B\right)\ \left(0.25\right)^3$$
$$\left(C\right)\ \left(0.25\right)^6$$
$$\left(D\right)\ \left(0.4\right)^3$$
$$\left(E\right)\ \left(0.8\right)^2$$

The OA is C.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

(1/8)^4 = (1/(2^3))^4 = 1/(2^12) = 1/(4^6) = (1/4)^6 = (0.25)^6

Answer: C

Scott Woodbury-Stewart
Founder and CEO
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