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

1 Answer
May 11, 2018

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