Answer
$a.) \ a - a^{\frac{33}{4}} $
$b.) \ x+2x^{\frac{1}{2}}-15$
Work Step by Step
$a.) \ a^{\frac{1}{4}}(a^{\frac{3}{4}}-a^8) = a^{\frac{1}{4}+\frac{3}{4}} - a^{\frac{1}{4}+8} = a^{\frac{4}{4}} - a^{\frac{33}{4}} = a - a^{\frac{33}{4}} $
$b.) \ (x^{\frac{1}{2}}-3)(x^{\frac{1}{2}}+5) = x^{\frac{1}{2}+\frac{1}{2}}+5x^{\frac{1}{2}}-3x^{\frac{1}{2}}-15= x+2x^{\frac{1}{2}}-15$
