Răspuns:
Explicație pas cu pas:
a)
= 2²⁺⁵⁺⁷=2¹⁴
b)
= (3³)²*(3²)³*3= 3⁶⁺⁶⁺¹=3¹³
c)
=7³⁰⁻¹⁰⁻²=7¹⁸
d)
=(2¹⁰⁺⁷)⁹:(2⁵⁺⁶)¹⁰=(2¹⁷)⁹:(2¹¹)¹⁰=2¹⁵³:2¹¹⁰=2¹⁵³⁻¹¹⁰=2¹⁴³
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2)
a)
4⁴⁷=(2²)⁴⁷=2⁹⁴
8³¹=(2³)³¹=2⁶²
2⁹⁴>2⁶²
4⁴⁷>8³¹
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b)
2⁵⁷*(2²-2-1)=2⁵⁷*1=2⁵⁷
3³⁸*(3²-3-5*1)=3³⁸*(9-3-5)=3³⁸*1=3³⁸
2⁵⁷=(2³)¹⁹=8¹⁹
3³⁸=(3²)¹⁹=9¹⁹
8¹⁹<9¹⁹
2⁵⁷<3³⁸
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3)
a)
= 27-9+1-1=18
b)
= (2²)³⁷:( 2¹⁺⁷¹) +318:106=2²ˣ³⁷: 2⁷²+3= 2⁷⁴:2⁷²+3=2⁷⁴⁻⁷²+3=2²+3=4+3=7
c)
3⁴⁸: (3²)⁹+((2²)⁴)⁵+6²³⁻¹³): [( 3²)⁵*(2⁵)²+3¹⁷⁺¹³+2⁵ˣ⁴=
(3⁴⁸:3¹⁸+2²⁰+6¹⁰): (3²ˣ⁵*(2⁵)²+3³⁰+2²⁰=
(3⁴⁸⁻¹⁸+2²⁰+6¹⁰): (3¹⁰*2¹⁰+3³⁰+2²⁰)=
(3³⁰+2²⁰+6¹⁰): [(3*2)¹⁰+3³⁰+2²⁰)}=
(3³⁰+2²⁰+6¹⁰): ( 3³⁰+2²⁰+6¹⁰)=1
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5)
a= 5⁴⁸*(5²+5+1)=5⁴⁸*(25+5+1)= 5⁴⁸*31 (unul din factori este 31 deci este patrat perfect
