Equivalent forms of exponential expressions

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Rewrite the expression $27^{ t }$ as $A⋅B^{ 1−3t }$

This is a problem from KhanAcademy.

Steps I took:

$9\cdot 3^{1-3t}=$

$9\cdot 3^{ 1}\cdot 3^{-3t } =$

$9\cdot 3^{ 1 }\cdot (\frac { 1 }{ 3^3 } )^{ t }=$

So at this point I feel lost and have no idea how to rewrite this expression. I must be doing something completely wrong from the beginning.

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1 Answer

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$27^t = 3^{3t} = 3\cdot \left(\dfrac{1}{3}\right)^{1-3t}$. Can you tell what $A$, and $B$ are?

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