Rewrite (1/27)^x as a base of three.....

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- Jul 27th 2006, 01:43 PMLuckyjoshuaanother one...help!
Rewrite (1/27)^x as a base of three.....

HELP! - Jul 27th 2006, 01:55 PMtopsquarkQuote:

Originally Posted by**Luckyjoshua**

$\displaystyle \left ( \frac{1}{27} \right ) ^x = \left ( \frac{1}{3^3} \right ) ^x$

$\displaystyle = \left ( \left [ \frac{1}{3} \right ] ^3 \right )^x$

$\displaystyle = \left ( \frac{1}{3} \right ) ^{3 \cdot x} = \left ( \frac{1}{3} \right ) ^{3x}$

Again, $\displaystyle \frac{1}{3} = 3^{-1}$ which results (via the same kind of method) to

$\displaystyle \left ( \frac{1}{27} \right ) ^x = 3^{-3x}$

-Dan