Question

Aflati (a, b), [a, b], stiind ca:
a=[(20• 25^{200} )•( 2^{100} • 10^{3} )]:( 2^{100} • 5^{400} •250)

b=(6+2)•[(3• 5^{2} - 2^{2} •18: 3^{2} +3•11): 2^{2}

Answer 1

a=[2²· 5 ·(5²)²⁰⁰·  2¹⁰⁰· 2³ ·5³ ] : [ 2¹⁰⁰ ·5⁴⁰⁰ · 2· 5³ ] = [ 2²⁺¹⁰⁰⁺³ · 5¹⁺⁴⁰⁰⁺³ ] :
 : [ 2¹⁰⁰⁺¹ · 5⁴⁰⁰⁺³  ]  = [ 2 ¹⁰⁵· 5⁴⁰⁴ ] : [ 2¹⁰¹ · 5⁴⁰³ ] = 2 ¹⁰⁵⁻ ¹⁰¹· 5⁴⁰⁴⁻ ⁴⁰³ = 2⁴ 5¹  
b = 12 · [ 3· 25  - 4·18 :9 + 33 ] : 4 
   = 12 · [ 75  - 4· 2 + 33 ]: 4 
     =12 · [ 75 - 8 + 33 ] : 4 = 12 ·100 :4 =12 · 25 = 2²· 3 · 5²
( a , b ) = 2²·5 =20
[a, b ] = 2⁴· 3·5² =16 ·3· 25 = 1200