Question

Show that `(8x^2)^(8-r)(1/(2x))^r=2^(24-4r)(x^(16-3r))`?

Answer 1

`LHS=(8x^2)^(8-r)*(1/(2x))^r`

`=[(2^3*x^2)^(8-r)][((2x)^(-1))^r]`

`=[2^(3(8-r))*x^(2(8-r))][(2x)^-r]`

`=[2^(24-3r)*x^(16-2r)][2^(-r)*x^(-r)]`

`=2^(24-3r-r)*x^(16-2r-r)=2^(24-4r)*x^(16-3r)=RHS`