Question

(8 la puterea 37 x 81 la puterea 25) : (16 la puterea 27 x 27 la puterea 33) =

Answer 1

(...)₁  ...   8³⁷ = (2³)³⁷=2¹¹¹ ;   81²⁵ = (3⁴)²⁵=3¹⁰⁰  ;
(...)₂  ...  16²⁷=(2⁴)²⁷=2¹⁰⁸ ;   27³³=(3³)³³=3⁹⁹   ;
avem:  (2¹¹¹ * 3¹⁰⁰) :(2¹⁰⁸ * 3⁹⁹) = 2¹¹¹⁻¹⁰⁸ * 3¹⁰⁰⁻⁹⁹ = 2³ * 3¹ = 8 * 3 =24

Answer 2

$(8^3^7 \cdot 81^2^5):(16^2^7 \cdot 27^3^3)=[(2^3)^3^7 \cdot (3^4)^2^5]:[(2^4)^2^7 \cdot (3^3)^3^3]= \\ =(2^1^1^1 \cdot 3^1^0^0):(2^1^0^8 \cdot 3^9^9)=2^{111-108}\cdot 3^{100-99}= 2^3\cdot 3^1=8 \cdot 3=24$