Question

Which is the simplified form of the expression ((p squared) (q Superscript 5 Baseline)) Superscript negative 4 Baseline times ((p Superscript negative 4 Baseline) (q Superscript 5 Baseline)) Superscript negative 2?
StartFraction 1 Over q Superscript 30 Baseline EndFraction
q Superscript 30
StartFraction p Superscript 12 Baseline Over q Superscript 60 Baseline EndFraction
p Superscript 12 Baseline q Superscript 60

Answer 1

((p^2 q^5)^{-4})( (p^{-4} q^5)^{-2})
= p^{2(-4)} q^{5(-4)} · p^{-4(-2)} q^{5(-2)}
= p^{-8} q^{-20} · p^{8} q^{-10}
= p^{0} q^{-30}
= 1/q^{30}.

So the simplified form is 1/q^30.