Exponents

**devi** · August 18th 2008, 09:22 PM

The value of (32/243)^-3/5 is
(a)27/8
(b)8/27
(c)16/27
Pls explain.

**CaptainBlack** · August 18th 2008, 09:49 PM

Originally Posted by devi

The value of (32/243)^-3/5 is
(a)27/8
(b)8/27
(c)16/27
Pls explain.

32=2^5 and 243=3^5, so:

(32/243)^(-3/5)=(2/3)^(-3)=(3/2)^3=27/8

RonL

**o_O** · August 18th 2008, 09:51 PM

Remember that: $\displaystyle a^{\frac{s}{t}} = \displaystyle \sqrt[t]{a^{s}} = \displaystyle\left(\sqrt[t]{a}\right)^{s}$

Here,
$\left(\frac{32}{243}\right)^{-\frac{3}{5}} = \underbrace{\left(\frac{243}{32}\right)^{\frac{3}{ 5}}}_{\displaystyle a^{-m} = \displaystyle \frac{1}{a^{ m}}} = \left(\frac{243^{3/5}}{32^{3/5}}\right) = ...$

Can you finish?

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