1
Daraja va uning xossalari
maktab darsligi: algebra 7-sinf, daraja; algebra 8-sinf, butun ko‘rsatkichli daraja
Maqsad: Daraja xossalarini ishlatib ifodalarni tez hisoblash.
Qoida va g‘oya
a^n — a sonini n marta o‘ziga ko‘paytirish. Xossalar (a ≠ 0, asoslari bir xil bo‘lsa): a^m · a^n = a^(m+n); a^m : a^n = a^(m−n); (a^m)^n = a^(m·n); (ab)^n = a^n · b^n; (a/b)^n = a^n / b^n. Maxsus holatlar: a^0 = 1 (a ≠ 0), a^(−n) = 1 / a^n. Manfiy asosli darajada ishora ko‘rsatkichning juft yoki toq bo‘lishiga bog‘liq: (−2)^4 = 16, (−2)^3 = −8. Eslab qoling: −2^4 = −16, chunki daraja minusdan oldin bajariladi. Ifodani avval bir asosga keltiring, so‘ng ko‘rsatkichlar ustida amal bajaring.
Namunaviy masalalar
2^5 · 2^3 : 2^6 ni hisoblang.
Yechim: Ko‘rsatkichlar: 5 + 3 − 6 = 2. 2^2 = 4.
Javob: 4
Yechim: Ko‘rsatkichlar: 5 + 3 − 6 = 2. 2^2 = 4.
Javob: 4
(3/2)^(−3) ni hisoblang.
Yechim: Teskari kasrga o‘tamiz: (2/3)^3 = 8/27.
Javob: 8/27
Yechim: Teskari kasrga o‘tamiz: (2/3)^3 = 8/27.
Javob: 8/27
(2^3)^2 : 4^2 ni hisoblang.
Yechim: (2^3)^2 = 2^6 = 64. 4^2 = 16. 64 : 16 = 4.
Javob: 4
Yechim: (2^3)^2 = 2^6 = 64. 4^2 = 16. 64 : 16 = 4.
Javob: 4
Tipik xatolar
- Ko‘paytirishda ko‘rsatkichlarni ko‘paytirish: a^m · a^n = a^(m+n), a^(m·n) emas.
- −3^2 ni 9 deb olish: aslida −3^2 = −9, (−3)^2 = 9.
- a^0 = 0 deb o‘ylash: 0 emas, 1 ga teng.
Mashq
1
2^3 · 2^4 : 2^5 ni hisoblang.
4
2
3^(−2) ni hisoblang.
1/9
3
(−2)^4 + (−2)^3 ni hisoblang.
8
4
10^3 · 10^(−5) ni hisoblang.
0,01