# Negative and rational powers

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• July 24th 2009, 04:24 PM
Mr Rayon
Negative and rational powers
Simplify the following, expressing your answer with positive index numbers

$
\frac{(-2)^{-3}\times2^{-4}}{2^{-3}}

$

Please show complete working out. Any help will be appreciated!
• July 24th 2009, 04:30 PM
yeongil
For even exponents n, $(-a)^n = a^n$.
For odd exponents n, $(-a)^n = -a^n$.

You should also know the properties of exponents, like
$a^m \times a^n = a^{m + n}$
and
$\frac{a^m}{a^n} = a^{m - n}$.

Apply the above to the problem. (I get $-\frac{1}{2^4}$ or $-\frac{1}{16}$ as my answer.)

01
• July 24th 2009, 04:52 PM
HallsofIvy
Quote:

Originally Posted by Mr Rayon
Simplify the following, expressing your answer with positive index numbers

$
\frac{(-2)^{-3}\times2^{-4}}{2^{-3}}

$

Please show complete working out. Any help will be appreciated!

First, $(-2)^{-3}= (-1(2))^{-3}= (-1)^{-3}2^{-3}$ and $(-1)^3= -1$
$a^{-3}= 1/a^3$ so this is the same as $-(2^{-3})(2^{-4})(2^3)$. Now use the fact that $a^na^m= a^{n+m}$.