To simplify this expression, we can follow the order of operations:
1. Simplify the expression inside the parentheses first:
(3x2^y - 2 - 7x2^(y-2))
2. Combine like terms:
3x2^y - 7x2^(y-2) - 2
3. Rewrite the denominator with a common base of 2:
5x2^(y-2)
4. Divide the numerator by the denominator:
(3x2^y - 7x2^(y-2) - 2) ÷ (5x2^(y-2))
5. Simplify by dividing each term in the numerator by 5x2^(y-2):
(3x2^y)/(5x2^(y-2)) - (7x2^(y-2))/(5x2^(y-2)) - (2/(5x2^(y-2)))
6. Simplify the exponents:
(3/5)x^(y-2) - (7/5) - (2/5)x^(-2)
So the final simplified expression is:
(3/5)x^(y-2) - (7/5) - (2/5)x^(-2)