SOLUTION: Can someone please show me ALL the steps to do this???? Find the zero(s) of the function y=3(^-2(x-4)-sqrt27 without using technology. Just to be clear, the exponent next to the

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Question 126919: Can someone please show me ALL the steps to do this????
Find the zero(s) of the function y=3(^-2(x-4)-sqrt27 without using technology.
Just to be clear, the exponent next to the three is -2(x-4).
I know the answer is x=13/4 but I don't understand completely and I would appreciate any help I can get :)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y=3%5E%28-2%28x-4%29%29-sqrt%2827%29
3%5E%28-2%28x-4%29%29-sqrt%2827%29=0Set y=0.
3%5E%28-2%28x-4%29%29=sqrt%283%2A3%2A3%2927 is also 3*3*3.
3%5E%28-2%28x-4%29%29=sqrt%283%5E3%293*3*3 is 3^3.
3%5E%28-2%28x-4%29%29=%283%5E3%29%5E%281%2F2%29The square root is to the (1/2) power.
3%5E%28-2%28x-4%29%29=3%5E%283%2F2%29 The same base, the exponents must equal each other.
-2%28x-4%29=3%2F2Set exponents equal to each other.
x-4=-3%2F4Divide both sides by (-2).
x=-3%2F4%2B4Add 4 to both sides.
x=-3%2F4%2B16%2F4Add and subtract fractions, need same denominator.
x=%28-3%2B16%29%2F4Same denominator, add or subtract numerators.
x=13%2F4Final answer.