The operation of exponent and exponent power

The operation of exponent and exponent power

Multiplication of the power of the same base number: the base number remains unchanged, and the exponentially added number
Division of the power of the same base number: the base number remains unchanged and the index is subtracted
The power of power: constant base, exponentially multiplied
Power of the product: equal to the product of the respective powers of the factors
The power of quotient (fractional power): the power of numerator and denominator respectively, and the index unchanged

On the operation of exponent and power
Given (2 ^ x) + (2 ^ - x) = a, how much does (8 ^ x) + (8 ^ - x) equal?
Note: 2 ^ x is the x power of 2, 2 ^ - x is the - x power of 2, the same as 8 ^ X
Why do two people have different answers? Who is right?

2 ^ x + 2 ^ (- x) = a, the square of both sides is 2 ^ (2x) + 2 ^ (- 2x) + 2 = A & sup2;, then 2 ^ (2x) + 2 ^ (- 2x) = A & sup2; - 2,8 ^ x + 8 ^ (- x) = 2 ^ (3x) + 2 ^ (- 3x) = [2 ^ x + 2 ^ (- x)] [2 ^ (2x) - 2 ^ x * 2 ^ (- x) + 2 ^ (- 2x)] = [2 ^ x + 2 ^ (- x)] [2 ^ (2x) - 1 + 2 ^ (- 2x) = [2 ^ x + 2 ^ (- 2x)]

On the operation of exponent and exponential power
The following formula holds true
A. a√－a＝√－a³
B. a√－a＝－√a³
C.a√－a＝－√－a³
D.a√－a＝√a³

A