Math Help - exponent and bases

1. another one...help!

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

HELP!

2. Originally Posted by Luckyjoshua
Rewrite (1/27)^x as a base of three.....

HELP!
$27 = 3^3$ so...

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

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

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

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

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

-Dan