# Math Help - Index Notation

1. ## Index Notation

I think im just being stupid, but i can't get my head around a index calculation:

(27/8)^2/3

Im just not sure exactly how to do these types, i know 27^2/3 would be 9, but i don't see what it would be when its a fraction, this is supposed to be done without a calculator.

2. Originally Posted by Joluk
I think im just being stupid, but i can't get my head around a index calculation:

(27/8)^2/3

Im just not sure exactly how to do these types, i know 27^2/3 would be 9, but i don't see what it would be when its a fraction, this is supposed to be done without a calculator.
We know that
$\left ( \frac{a}{b} \right ) ^n = \frac{a^n}{b^n}$
(with suitable conditions on a, b, and n.)

So
$\left ( \frac{27}{8} \right )^{2/3} = \frac{27^{2/3}}{8^{2/3}} = \frac{9}{4}$

-Dan

3. Ahhh, *bangs head against desk*

Thanks

4. Originally Posted by Joluk