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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.
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July 26th, 2018, 10:15 AM   #2
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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:

$\displaystyle \frac{a^{\Large\frac{1}{2}}}{a^{-\Large\frac{3}{2}}}=a^{\Large\frac{1}{2}}\cdot a^{\Large\frac{3}{2}}=a^{\Large\frac{1}{2}+\frac{3 }{2}}=a^2$
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July 26th, 2018, 12:58 PM   #3
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Quote:
Originally Posted by DennisSally View Post
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.
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July 26th, 2018, 08:41 PM   #4
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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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