My Math Forum Fractional Indices - Help!

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July 26th, 2018, 09:46 AM   #1
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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).
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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: 12,204 Thanks: 511 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: $\displaystyle \frac{a^{\Large\frac{1}{2}}}{a^{-\Large\frac{3}{2}}}=a^{\Large\frac{1}{2}}\cdot a^{\Large\frac{3}{2}}=a^{\Large\frac{1}{2}+\frac{3 }{2}}=a^2$ Thanks from greg1313, topsquark and DennisSally
July 26th, 2018, 12:58 PM   #3
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Quote:
 Originally Posted by DennisSally 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).
Two points.

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: 19,722 Thanks: 1807 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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