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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 its 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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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 its 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?
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July 26th, 2018, 08:41 PM   #4
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Who mentioned indices?

What book is it that contains such questions, but doesn't also explain what methods are applicable?
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