C1 Indices

9x and 3 are fundamentally different, 9x is a coefficient of x whilst 3 is just a constant

Seeing as $2x^{\frac{2}{3}}$ and $x^{-1}$ are both coefficients of x, you can add the powers. But the coefficients in your other example are different and so you can't add the powers.

How come when you do 2x^2/3 x 3x^-1 You can multiply the 2 by the 3 and add the powers? But when you do 3¹⁰ x 9x¹⁵ you can't multiply 3 by 9 and then add the powers?