Potęgi

Wzór Przykład
a0=1a^0=1 70=15^0=1
a1=aa^1=a 71=77^1=7
a−1=1aa^{-1}=\frac{1}{a} 5−1=155^{-1}=\frac{1}{5}
(ab)−1=ba\left(\frac{a}{b}\right)^{-1}=\frac{b}{a} (34)−1=43\left(\frac{3}{4}\right)^{-1}=\frac{4}{3}
(ax)y=ax⋅y\left(a^x\right)^y=a^{x\cdot y} (62)3=66\left(6^2\right)^3=6^6
ax⋅ay=ax+ya^x\cdot a^y=a^{x+y} 43⋅46=494^3\cdot4^6=4^9
ax:ay=ax−ya^x:a^y=a^{x-y} 104:102=10210^4:10^2=10^2
ax⋅bx=(a⋅b)xa^x\cdot b^x=\left(a\cdot b\right)^x 32⋅22=(3⋅2)2=623^2\cdot 2^2=\left(3\cdot 2\right)^2=6^2
axbx=(ab)x\frac{a^x}{b^x}=\left(\frac{a}{b}\right)^x 15353=(155)3=33\frac{15^3}{5^3}=\left(\frac{15}{5}\right)^3=3^3