Simplify the following, expressing your answer with positive index numbers

$\displaystyle

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

$

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

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- Jul 24th 2009, 04:24 PMMr RayonNegative and rational powers
Simplify the following, expressing your answer with positive index numbers

$\displaystyle

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

$

Please show complete working out. Any help will be appreciated! - Jul 24th 2009, 04:30 PMyeongil
For even exponents n, $\displaystyle (-a)^n = a^n$.

For odd exponents n, $\displaystyle (-a)^n = -a^n$.

You should also know the properties of exponents, like

$\displaystyle a^m \times a^n = a^{m + n}$

and

$\displaystyle \frac{a^m}{a^n} = a^{m - n}$.

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

01 - Jul 24th 2009, 04:52 PMHallsofIvy