An equation is shown.

A^6 * a^-3 = (a^?) ^2

A⁶ · a⁻³ = (a^ (³/₂)) ²

a⁶ = a³

a³

a³ = a³

Properties of exponents say that when multiply powers, you add them, so A^6*A^-3=3 and porperties of exponents also say that when raising a power to a power, you multiply them, so (A^?) ^2 is really just?*2. We take the three from the left equation and set it equal to the right equation so we get, 3=?*2. solve for?.

?=1.5