1.2-bo'lim : Ratsional ko'rsatkichlar
5. Quyidagi ifodani baholang va javobni darajasiz bitta son shaklida yozing.
\[{\left( {\frac{9}{4}} \right)^{\frac{1}{2}}}\]
Maslahat: Asosiy eksponent qoidalarini va birinchi ikkita mashq muammosi qanday ishlaganligini unutmang.
Yechim
Keling, birinchi navbatda asosiy ko'rsatkich qoidalarini eslaylik va buni osongina yozishimiz mumkinligini ta'kidlaymiz:
\[{\left( {\frac{9}{4}} \right)^{\frac{1}{2}}} = \frac{{{9^{\frac{1}{2}}}}}{{{4^{\frac{1}{2}}}}}\]2-qadam
Endi, dastlabki ikkita amaliyot muammosi qanday ishlaganini eslab, buni ko'rishimiz mumkin,
\[{9^{\frac{1}{2}}} = 3\hspace{0.25in}\hspace{0.25in}\hspace{0.25in}{4^{\frac{1}{2}}} = 2\]Shuning uchun,
\[{\left( {\frac{9}{4}} \right)^{\frac{1}{2}}} = \frac{{{9^{\frac{1}{2}}}}}{{{4^{\frac{1}{2}}}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{3}{2}}}\]