1.2-bo'lim : Ratsional ko'rsatkichlar
9. Quyidagi ifodani soddalashtiring va javobni faqat musbat darajalar bilan yozing.
\[{\left( {\frac{{{q^3}\,{p^{ - \frac{1}{2}}}}}{{{q^{ - \frac{1}{3}}}\,p}}} \right)^{\frac{3}{7}}}\]Yechim
Bu erda soddalashtirish uchun oldingi bo'limdagi ko'rsatkich xususiyatlaridan foydalanishdan boshqa ko'p ish yo'q.
\[{\left( {\frac{{{q^3}\,{p^{ - \frac{1}{2}}}}}{{{q^{ - \frac{1}{3}}}\,p}}} \right)^{\frac{3}{7}}} = {\left( {\frac{{{q^3}\,{q^{\frac{1}{3}}}}}{{\,p{p^{\frac{1}{2}}}}}} \right)^{\frac{3}{7}}}\, = {\left( {\frac{{{q^{\frac{{10}}{3}}}}}{{\,{p^{\frac{3}{2}}}}}} \right)^{\frac{3}{7}}}\, = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{{q^{\frac{{10}}{7}}}}}{{\,{p^{\frac{9}{{14}}}}}}}}\]