Question

Va rog exercitiul 23!!

Answer 1

a)  {{[(1+2+3+..100): 1010]²⁰⁰² *5³ :5²⁰⁰³}³ -5⁵} :10² +5=

={{[ (100*101/2):1010]²⁰⁰² *5³ :5²⁰⁰³}³ -5⁵} :10² +5=

={[[ (5050:1010)²⁰⁰² *5³ :5²⁰⁰³]³ -5⁵} :10² +5=

= [ (5²⁰⁰² *5³ :5²⁰⁰³)³ -5⁵] :10² +5=[(5²⁰⁰⁵ : 5²⁰⁰³)³ -5⁵] :10² +5= (5⁶-5⁵):10²+5=

= 5⁵(5-1):10²+5= 25*4 : 100+5=1+5=6

b) (2¹)²*{3⁴ *28 -[3 -(2³*5³- 3²*10²-5²) : (9+4²)] :10⁴  -2²^⁰*3⁴}=

=2²*{3⁴ *28 -[3 -5²*(2³*5- 3²*2²-1) : (9+16)] :10⁴  -2¹*81}=

= 4*{81 *28 -[3 -25*(40- 36-1) : 25] :10⁴  -162}=

= 4*[81 *28 -(3 -25*3 : 25) :10⁴  -162]= 4*[81 *28 -(3 -3) :10⁴  -162]=

=4*(2268 -0  -162)=4*2106=8424

c)2¹⁰¹: [ (3*5 -13)⁹⁸+2¹⁰⁵ : (2³*16)+8³³]*23=2¹⁰¹: [ (15 -13)⁹⁸+2¹⁰⁵ : (2³*2⁴)+(2³)³³]*23=

=2¹⁰¹: ( 2⁹⁸+2¹⁰⁵ : 2⁷+2⁹⁹) *23= 2¹⁰¹ : (2⁹⁸+2⁹⁸+2⁹⁹)*23=2¹⁰¹ : [2⁹⁸(1+1+2)]*23=

=2¹⁰¹: ( 2⁹⁸*2²)*23=2¹⁰¹: 2¹⁰⁰^*23=2*23=46