Math CentralQuandaries & Queries


Question from Chelsea

(81 to the power of 3n+2 over 243 to the power of -n) is equal to 3 to the power of 4
Find the value of n.
The answer I got was n is equal to negative (4 over 7).
The answer in my text was n is equal to negative (4 over 17)

Hi Chelsea,

I also get $- \frac{4}{17}.$

$243 = 3^5$ and $81 = 3^4$ so

\[\frac{81^{3n + 2}}{243^{-n}}\]


\[\left( 3^4 \right)^{3n + 2} \times \left( 3^5 \right)^n = 3^4\]

Is that what you did?


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