1.2-bo'lim : Ratsional ko'rsatkichlar
3. Quyidagi ifodani baholang va javobni darajasiz bitta son shaklida yozing.
\[ - {16^{\frac{3}{2}}}\]
Maslahat: Asosiy eksponent qoidalarini va birinchi ikkita mashq muammosi qanday ishlaganligini unutmang. Bundan tashqari, ushbu muammoda minus belgilar bilan ehtiyot bo'ling.
Yechim
Birinchidan, muammoni quyidagicha yozamiz:
\[ - \left( {{{16}^{\frac{3}{2}}}} \right)\]shuning uchun biz eksponentga minus belgisini olib kelish vasvasasiga tushmaymiz.
Keling, asosiy ko'rsatkich qoidalarini eslaylik va buni osongina yozishimiz mumkinligini ta'kidlaymiz:
\[ - \left( {{{16}^{\frac{3}{2}}}} \right) = - \left( {{{\left( {{{16}^{\frac{1}{2}}}} \right)}^3}} \right)\]2-qadam
Endi, dastlabki ikkita amaliyot muammosi qanday ishlaganini eslab, buni ko'rishimiz mumkin,
\[{16^{\frac{1}{2}}} = 4\]chunki \({4^2} = 16\).
Shuning uchun,
\[ - {16^{\frac{3}{2}}} = - \left( {{{16}^{\frac{3}{2}}}} \right) = - \left( {{{\left( {{{16}^{\frac{1}{2}}}} \right)}^3}} \right) = - \left( {{{\left( 4 \right)}^3}} \right) = - \left( {64} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{ - 64}}\]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.