If (a^x)^2/3=1[numerator]/a^2[denominator] then what is the value of x

options :
a.1
b.2
c.-3
d.-1

Hint 1: (a^m)^n = a^(mn)
Hint 2: 1/a^n = a^(-n)
Hint 3: if a^m = a^n and a≠±1 then m=n

(a^x)^2/3 = 1/a² : Hint 1 , Hint 2
a^(x * 2/3) = a-² : Hint 3 (only if a≠±1 )
(x * 2/3) = -2
x = -2 * 3/2
x = -3

Using the rule that, to raise a power to a power, multiply the exponents
[i.e. (a^m)^n = a^(mn)]:

(a^x)^(2/3)
= a^(2x/3)

Using the fact that a negative exponent indicates reciprocal
[ i.e. a^(-n) = 1/(a^n) ]
we have
1/(a^2) = a^(-2)

Comparing the two,
2x/3 = -2
Therefore
2x = -6
x = -3