1)1+2+3+...+73=73·74/2=2701(suma lui gausse)
2)b¹³·b¹·b²¹·b²⁰=b¹³⁺¹⁺²¹⁺²⁰=b⁵⁵ (nᵃ·nᵇ=nᵃ⁺ᵇ)
3)c⁵⁸ : c³⁹ : c⁹=c⁵⁸⁻³⁹⁻⁹=c¹⁰ (nᵃ : nᵇ=nᵃ⁻ᵇ)
4)125⁴² : 25⁶³=(5³)⁴² : (5²)⁶³=5¹²⁶ : 5¹²⁶=1
(nᵃ)ᵇ=nᵃ·ᵇ(n la puterea a ori b)
125=5³
25=5²
5)(8³⁷·81²⁵) : (16²⁷·27³³)=
=[(2³)³⁷·(3⁴)²⁵] : [(2⁴)²⁷·(3³)³³]=
=2¹¹¹·3¹⁰⁰: 2¹⁰⁸·3⁹⁹=
=2¹¹¹⁻¹⁰⁰·3¹⁰⁰⁻⁹⁹=
=2¹¹·3
6)2¹·2²·2³·...·2⁴⁵=
=2¹⁺²⁺³⁺···⁺⁴⁵=
[tex] =2^{ \frac{45*46}{2} } [/tex]
=2¹⁰³⁵
bafta! :D