If (frac{27^x times 3^{1 – x}}{9^{2x}} = 1), find the value of x.

A.
1 
B.
(frac{1}{2}) 
C.
(frac{1}{2}) 
D.
1
Correct Answer: Option B
Explanation
(frac{27^x times 3^{1 – x}}{9^{2x}} = 1)
(frac{3^{3x} times 3^{1 – x}}{3^{2(2 – x)}} = 3^0)
(3^{3x} times 3^{1 – x} div 3^{4x} = 3^0)
(3^{(3x + 1 – x – 4x)} = 3^0)
(3^{(1 – 2x)} = 3^0)
since the bases are equal,
1 – 2x = 0
– 2x = 1
x = (frac{1}{2})