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# Integers $m$ and $n$ satisfy the equation $6^m 3^n=2592$. What is the value of $6^n3^m$?

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Integers $m$ and $n$ satisfy the equation $6^m 3^n=2592$. What is the value of $6^n3^m$?

Nov 17, 2020

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Integers $m$ and $n$ satisfy the equation $6^m 3^n=2592$. What is the value of $6^n3^m$?

Hello Guest!

$$6^m 3^n=2592\\$$

6 36 216 1296 7776

9    27     81   243

$$6^5\cdot 3^{-1}=2592$$

The value of $$6^m 3^n=2592$$ is

$$m=5\\ n=-1$$

!

Nov 17, 2020