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July 26th, 2018, 09:46 AM  #1 
Newbie Joined: Jul 2018 From: Scotland Posts: 1 Thanks: 0  Fractional Indices  Help!
I have attempted a question a couple of times and it's grinding my gears  any help? I attached the question as a picture to avoid confusion. The book says the answer is supposed to be (a^2).
Last edited by skipjack; August 22nd, 2018 at 10:24 AM. 
July 26th, 2018, 10:15 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs 
We are given the expression: $\displaystyle \frac{a^{\Large\frac{1}{2}}}{a^{\Large\frac{3}{2}}}$ A rule for exponents is: $\displaystyle r^{s}=\frac{1}{r^s}$ And so applying that rule, we may write: $\displaystyle \frac{a^{\Large\frac{1}{2}}}{a^{\Large\frac{3}{2}}}=a^{\Large\frac{1}{2}}\cdot a^{\Large\frac{3}{2}}$ Another rule for exponents is: $\displaystyle r^s\cdot r^t=r^{s+t}$ And so we may write: $\displaystyle \frac{a^{\Large\frac{1}{2}}}{a^{\Large\frac{3}{2}}}=a^{\Large\frac{1}{2}}\cdot a^{\Large\frac{3}{2}}=a^{\Large\frac{1}{2}+\frac{3 }{2}}=a^2$ 
July 26th, 2018, 12:58 PM  #3  
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  Quote:
In North American English, what you call indices are called exponents. Are you asking what fractional exponents mean? Last edited by skipjack; August 22nd, 2018 at 10:25 AM.  
July 26th, 2018, 08:41 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,975 Thanks: 2224 
DennisSally put "indices" in the title only, but apparently is from Scotland anyway. What book is it that contains such questions, but doesn't also explain what methods are applicable? Last edited by skipjack; August 22nd, 2018 at 10:31 AM. 

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