1.2-bo'lim : Ratsional ko'rsatkichlar
6. Quyidagi ifodani baholang va javobni darajasiz bitta son shaklida yozing.
\[{\left( {\frac{8}{{343}}} \right)^{ - \frac{2}{3}}}\]
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:
\[{\left( {\frac{8}{{343}}} \right)^{ - \frac{2}{3}}} = {\left( {\frac{{343}}{8}} \right)^{\,\frac{2}{3}}} = \frac{{{{343}^{\frac{2}{3}}}}}{{{8^{\frac{2}{3}}}}} = \frac{{{{\left( {{{343}^{\frac{1}{3}}}} \right)}^2}}}{{{{\left( {{8^{\frac{1}{3}}}} \right)}^2}}}\]2-qadam
Endi, dastlabki ikkita amaliyot muammosi qanday ishlaganini eslab, buni ko'rishimiz mumkin,
\[{343^{\frac{1}{3}}} = 7\hspace{0.25in}\hspace{0.25in}\hspace{0.25in}{8^{\frac{1}{3}}} = 2\]Shuning uchun,
\[{\left( {\frac{8}{{343}}} \right)^{ - \frac{2}{3}}} = {\left( {\frac{{343}}{8}} \right)^{\,\frac{2}{3}}} = \frac{{{{343}^{\frac{2}{3}}}}}{{{8^{\frac{2}{3}}}}} = \frac{{{{\left( {{{343}^{\frac{1}{3}}}} \right)}^2}}}{{{{\left( {{8^{\frac{1}{3}}}} \right)}^2}}} = \frac{{{7^2}}}{{{2^2}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{49}}{4}}}\]