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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Which of the following equivalent to (1/8)^4? tagged by: AAPL ##### This topic has 2 expert replies and 0 member replies ### Top Member ## Which of the following equivalent to (1/8)^4? 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. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 497 members Upvotes: 2867 GMAT Score: 800 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 Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: 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. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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