simplify (4a 4 ) -3/2 /(b 2 )

Move the negative exponent in the numerator to the denominator. 1/[(4a 4 ) 3/2 *b 2 ] = 1/[4 3/2 *(a 4 ) 3/2 *b 2 ] = 1/[8*a 6 b 2 ].