exponent and bases

**Luckyjoshua** · July 27th 2006, 01:43 PM

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

HELP!

**topsquark** · July 27th 2006, 01:55 PM

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

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