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I am having a problem with the following question:

If $$N = 3^P { } $$ and $$M=P-1$$ Then in terms of M what is $$ \frac{3}{N}=?$$

Any suggestions on which properties to apply ?

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Note that $\dfrac{3}{N}=\dfrac{3}{3^P}=\dfrac{1}{3^{P-1}}$. Or else more simply use $P=M+1$, so $3^P=3^{M+1}$. – André Nicolas Jul 10 '12 at 17:47
up vote 0 down vote accepted

Simply substitute and use exponents' laws: $$N=3^P\,,\,M=P-1\Longrightarrow \frac{3}{N}=\frac{3}{3^P}=\frac{1}{3^{P-1}}=\frac{1}{3^M}$$

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