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