Answer:
(i) x = 1/2
(ii) x^-2 = (2/3)^12
Explanation:
Part 1
Preceding from given question:
As bases are same so powers will be added as follows:
(2/3)^2x+1 + x = (3/2)^-2-x
Or
(2/3)^3x+1 = (3/2)^-(2+x)
By inverting right fraction
(2/3)^3x+1 = (2/3)^2+x
Now both bases are same so cancel out them
3x + 1 = 2 + x
3x - x = 2 - 1
2x = 1
x = 1/2
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Part 2
Preceding from given question:
The fraction on right will be inverted and sign will be changed
x = (3/2)^2 * (3/2)^4
Bases are same so powers will be added
x = (3/2)^6 = 729/ 64 ---------- eq1
We have to find x^-2 so
x^-2 = (729/64)^-2
by inverting to change negative sign
x^-2 = (64/729)^2
OR
Using eq1:
x^-2 = (2/3)^12
i hope it will help you!