Tính chất cơ bản

1) an = a × {\displaystyle \times } a × {\displaystyle \times } a × {\displaystyle \times } ... × {\displaystyle \times } a

n chữ số a

2) a − n = 1 a n = 1 a × a × a × . . . a {\displaystyle a^{-n}={\frac {1}{a^{n}}}={\frac {1}{a\times a\times a\times ...a}}}

3) 0n = 0 (n > 0)

4) 1n = 1

5) a0 = 1

6) a1 = a

7) a − 1 = 1 a {\displaystyle a^{-1}={\frac {1}{a}}}

Tính chất thường găp

1) am + n = am × {\displaystyle \times } an

2) a m − n = a m a n {\displaystyle a^{m-n}={\frac {a^{m}}{a^{n}}}} với mọi a ≠ 0

3) a m ⋅ n = ( a m ) n {\displaystyle a^{m\cdot n}=(a^{m})^{n}}

4) a m n = a ( m n ) {\displaystyle a^{m^{n}}=a^{(m^{n})}}

5) ( a × b ) n = a n × b n {\displaystyle (a\times b)^{n}=a^{n}\times b^{n}}

6) ( a b ) n = a n b n {\displaystyle ({\frac {a}{b}})^{n}={\frac {a^{n}}{b^{n}}}}

7) a m / n = ( a m ) 1 / n = a m n {\displaystyle a^{m/n}=\left(a^{m}\right)^{1/n}={\sqrt[{n}]{a^{m}}}}

8) a x = e x ⋅ ln ⁡ a {\displaystyle a^{x}=e^{x\cdot \ln a}\,}

9) e i x = cos ⁡ x + i ⋅ sin ⁡ x {\displaystyle e^{ix}=\cos x+i\cdot \sin x}