9 to the power of 2x+1=81 to the power of x ÷3 to the power of x

Answer 1

If you mean

9^(2x+1) = 81^x / 3^x
expressing all as powers of 3, we have

3^(4x+2) = 3^3x
so,
4x+2 = 3x
x = -2

check:

9^-3 = 81^-2 / 3^-2 = 9^-4/9^-1 = 9^-3