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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 ## Complicated exponent tagged by: Brent@GMATPrepNow ##### This topic has 3 expert replies and 1 member reply Problem: (x^-5/x^-9)^1/2. The answer is x2, but here is my confusion To do this problem my first instinct was to just flip the fraction in the parenthesis, but someone I've been working with told me that's not possible. There approach was to multiply the denominator by a negative fraction, and then multiply. But I'm still confused as to why his version is right and mine is wrong ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13033 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 GeauxSwish wrote: Problem: (x^-5/x^-9)^1/2. The answer is x2, but here is my confusion To do this problem my first instinct was to just flip the fraction in the parenthesis, but someone I've been working with told me that's not possible. There approach was to multiply the denominator by a negative fraction, and then multiply. But I'm still confused as to why his version is right and mine is wrong IMPORTANT RULES Division Rule: (x^a)/(x^b) = x^(a-b) Power of a Power Rule: (x^a)^b = x^(ab) (x^-5/x^-9)^1/2 = (x^(-5 - -9))^1/2 [Division Rule] = (x^4)^1/2 = x^(4 times 1/2) [Power of a Power Rule] = x^2 Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! Junior | Next Rank: 30 Posts Joined 29 Dec 2016 Posted: 10 messages Brent@GMATPrepNow wrote: GeauxSwish wrote: Problem: (x^-5/x^-9)^1/2. The answer is x2, but here is my confusion To do this problem my first instinct was to just flip the fraction in the parenthesis, but someone I've been working with told me that's not possible. There approach was to multiply the denominator by a negative fraction, and then multiply. But I'm still confused as to why his version is right and mine is wrong IMPORTANT RULES Division Rule: (x^a)/(x^b) = x^(a-b) Power of a Power Rule: (x^a)^b = x^(ab) (x^-5/x^-9)^1/2 = (x^(-5 - -9))^1/2 [Division Rule] = (x^4)^1/2 = x^(4 times 1/2) [Power of a Power Rule] = x^2 Cheers, Brent So if I understand correct my way where I just flip the whole fraction so its x^9/x5 is just straight up illegal ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13033 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 GeauxSwish wrote: Brent@GMATPrepNow wrote: GeauxSwish wrote: Problem: (x^-5/x^-9)^1/2. The answer is x2, but here is my confusion To do this problem my first instinct was to just flip the fraction in the parenthesis, but someone I've been working with told me that's not possible. There approach was to multiply the denominator by a negative fraction, and then multiply. But I'm still confused as to why his version is right and mine is wrong IMPORTANT RULES Division Rule: (x^a)/(x^b) = x^(a-b) Power of a Power Rule: (x^a)^b = x^(ab) (x^-5/x^-9)^1/2 = (x^(-5 - -9))^1/2 [Division Rule] = (x^4)^1/2 = x^(4 times 1/2) [Power of a Power Rule] = x^2 Cheers, Brent So if I understand correct my way where I just flip the whole fraction so its x^9/x^5 is just straight up illegal Your way is correct. x^(-5) = 1/(x^5) and x^(-9) = 1/(x^9) So, (x^-5/x^-9) = [1/(x^5)]/[1/(x^9)] = [1/(x^5)]/[(x^9)/1] = x^9/x^5 _________________ Brent Hanneson – Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 12 Sep 2012 Posted: 2635 messages Followed by: 117 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 GeauxSwish wrote: So if I understand correct my way where I just flip the whole fraction so its x^9/x5 is just straight up illegal That's actually fine! You should get x⁹ / x⁵, which is the same thing as x⁴. All that's left is to take the square root of x⁴ (since you're raising to the 1/2 power, which is the same thing as taking the root), and you're done! Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. 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