Finding an exponential model $f ( x ) = a ( b ) ^ x$ satisfying $f ( 2 ) = 3$ and $f ( 5 ) = 54$

Given the points $$( 2 , 3 )$$ and $$( 5 , 54 )$$ are on an exponential model, find the equation for this model in the form $$f ( x ) = a ( b ) ^ x$$.

So I tried plugging in values so that $$3 = a ( b ) ^ 2$$ and $$54 = a ( b ) ^ 5$$ and divided the equations to get that $$b ^ 3 = 18$$. Then since $$b = \sqrt [ 3 ] { 18 }$$, I plugged in that value back to $$3 = a ( b ) ^ 2$$ to find that $$a = \frac { \sqrt { 12 } } { 12 }$$. However, when I used my calculators to check the values, the resulting function does not have points $$( 2 , 3 )$$ and $$( 5 , 54 )$$. How can I solve this problem?

Your $b$ is correct, but you should get $a = 3/b^2$ which is not $\sqrt{12}/12$.