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

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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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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

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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.
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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
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