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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 ## Exponential/power tagged by: BTGmoderatorRO ##### This topic has 1 expert reply and 0 member replies ## Exponential/power $$if\ \ \left(4^x\right)\left(8^y\right)\left(16^{7x}\right)=\left(8^{4y}\right)\left(32^x\right)\left(64^y\right)$$ $$what\ is\ the\ value\ of\ \ \frac{x}{y}\ ?$$ A. 3/5 B. 2/3 C. 3/4 D. 1 E. 4/3 OA is a which of the option here is accurate and best fit? kindly help me out Thank you ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: PRIOR POSTS IN THIS TOPIC Roland2rule Exponential/power Posted Fri Nov 03, 2017 12:16 am $$if\ \ \left(4^x\right)\left(8^y\right)\left(16^{7x}\right)=\left(8^{4y}\right)\left(32^x\right)\left(64^y\right)$$ $$what\ is\ the\ value\ of\ \ \frac{x}{y}\ ?$$ A. 3/5 B. 2/3 C. 3/4 D. 1 E. 4/3 OA is a which of the option here is accurate and best fit? kindly help me out Crying or Very sad Thank you Hi Roland2rule, Let's take a look at your question. $$\left(4^x\right)\left(8^y\right)\left(16^{7x}\right)=\left(8^{4y}\right)\left(32^x\right)\left(64^y\right)$$ $$\left(\left(2^2\right)^x\right)\left(\left(2^3\right)^y\right)\left(\left(2^4\right)^{7x}\right)=\left(\left(2^3\right)^{4y}\right)\left(\left(2^5\right)^x\right)\left(\left(2^6\right)^y\right)$$ $$\left(2^{2x}\right)\left(2^{3y}\right)\left(2^{28x}\right)=\left(2^{12y}\right)\left(2^{5x}\right)\left(2^{6y}\right)$$ $$\left(2^{2x+3y+28x}\right)=\left(2^{12y+5x+6y}\right)$$ $$\left(2^{30x+3y}\right)=\left(2^{5x+18y}\right)$$ Since, the base is the same on both sides of the equations, we can equate the exponents, therefore, $$30x+3y=5x+18y$$ $$30x+3y-5x=18y$$ $$25x+3y=18y$$ $$25x=18y-3y$$ $$25x=15y$$ $$\frac{x}{y}=\frac{15}{25}$$ $$\frac{x}{y}=\frac{3}{5}$$ Therefore, Option A 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 Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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