Question

1) 1+2+3+..........+73 =
2) b^13 x b x b^21 x b^20=
3) c^58 : c^39 : c^9=
4) 125^42 : 25^63=
5) (8^37 x 81 ^25 ) : (16^27 x 27^33) =
6) 2^1 x 2^2 x 2^3 x 2^4 x ..... x 2^45=
VA ROG AJUTOR ! NICIODATA NU AM INTELES ACESTE EXERCITII !!

Answer 1

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=
$=2^{ \frac{45*46}{2} }$
=2¹⁰³⁵
bafta! :D