Question

what is 3^square root 54

Answer 1

Thanks man!

Answer 2

Is that supposed to be \[3^\sqrt{54}\] or \[\sqrt[3]{54}\]

Answer 3

My guess is the latter...let's assume it is.

If we factor 54 into its prime components, we get
54 = 2*27 = 2*3*9 = 2*3*3*3
so \[\sqrt[3]{54} = \sqrt[3]{2*3*3*3}\]Remembering that if you have a square root, you can take out one of every pair of identical factors, what do you think you might do here with a cube root?
Hint: \[\sqrt[3]{8} = \sqrt[3]{2*2*2} = 2\]