1.2-bo'lim : Ratsional ko'rsatkichlar
4. Quyidagi ifodani baholang va javobni ko‘rsatkichsiz bitta son shaklida yozing.
\[{27^{ - \frac{5}{3}}}\]
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:
\[{27^{ - \,\,\frac{5}{3}}} = \frac{1}{{{{27}^{\frac{5}{3}}}}} = \frac{1}{{{{\left( {{{27}^{\frac{1}{3}}}} \right)}^5}}}\]2-qadam
Endi, dastlabki ikkita amaliyot muammosi qanday ishlaganini eslab, buni ko'rishimiz mumkin,
\[{27^{\frac{1}{3}}} = 3\]chunki \({3^3} = 27\).
Shuning uchun,
\[{27^{ - \,\,\frac{5}{3}}} = \frac{1}{{{{27}^{\frac{5}{3}}}}} = \frac{1}{{{{\left( {{{27}^{\frac{1}{3}}}} \right)}^5}}} = \frac{1}{{{{\left( 3 \right)}^5}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{1}{{243}}}}\]Ba'zida bunday muammolarni birinchi marta duch kelganingizda hal qilishning eng oson yo'li ularni bu erda qilganimiz kabi boshqarilishi mumkin bo'lgan bosqichlarga bo'lishdir.