Kipeo kinawakilisha kuzidisha mara kwa mara kwa nambari peke yake. Kwa mfano:
\(2^3\) , hapa 2 inaitwa 'msingi' na '3' ni kipeo kinachoonyesha ni mara ngapi msingi hutumika kama kipengele. Tunaweza pia kusema '2 kuinuliwa kwa uwezo wa 3'. Msingi wenye nguvu 2 na 3 una majina maalum. Kama \(2^2\) ni 'mraba 2' na \(2^3\) ni 'mchemraba 2'.
\(2^3 = 2 \times 2 \times 2\)
\(5^2 = 5 \times 5\)
\(6^4 = 6 \times 6 \times 6 \times 6\)
\(x^4 = x \times x \times x \times x\) , hapa x ni kigezo chenye kipeo 4
Sheria za kufuata katika kutatua usemi unaohusisha vielezi:
Kanuni ya 1: \(a^\frac{1}{n} = \sqrt[n]{a} \) (ambapo a ni nambari yoyote isiyo hasi)
\(27^\frac{1}{3} = \sqrt[3]{27}\)
\(64^\frac{1}{2} = \sqrt{64} = 8\)
Kanuni ya 2 : \(a^m \times a^n = a^{m+n} \) (a ni nambari halisi isiyo sifuri na m, n ni nambari kamili)
\(3^2 \times 3^1 = 3^{2+1} = 3^3 = 27\)
\(5^2 \times 5^2 = 5^{2+2} = 5^4 = 625\)
Kanuni ya 3 : \(a^m \div a^n = a^{mn} \) (a ni nambari halisi isiyo sifuri na m, n ni nambari kamili)
\(3^5 \div 3^2 = 3^{5-2} = 3^3 = 27\)
Kanuni ya 4: \((a^m)^n = a^{mn} \) (a ni nambari halisi isiyo sifuri na m, n ni nambari kamili)
\((2^2)^3 = 2^{2\times3} = 2^6 = 64\)
Kanuni ya 5 : \((a\times b)^m = a^m \times b^m\) (a ni nambari halisi isiyo sifuri na m ni nambari kamili)
\((2\times3)^2 = 2^2 \times 3^2=36\)
Kanuni ya 6 : \((\frac{a}{b})^m = a^m \div b^m\) (a, b: nambari halisi isiyo sifuri na m: nambari kamili)
\((\frac{12}{3})^2 = 12^2 \div 3^2 = 16\)
Kutumia sheria zilizo hapo juu pia ni kweli:
\(a^0 = 1\)
Mfano:
\(2^0 = 1 \text{ , } 6^0 = 1\)
\(a^{-m} = \frac{1}{a^m}\)
Mfano:
\(2^{-3} = \frac{1}{2^3}\)
