Question

efectueaza: a) (2^4-4^2)^100= b) (5^7:25^2-11^2)^10 :8^6 c) (1^100-100^0+3^100):9^7^2 d) (16⁴*8⁵:4¹⁵ +2°+2²)*4-5² e) (1⁰+1¹+1²+1³+...1¹⁰²)⁵:103³ f) (3¹⁵+9⁷):3¹⁴ g) (5¹²+25⁶+125⁴):5¹¹ h) (2²⁷:4⁶ +25⁴*2):(4⁷+5⁸) VA ROGGGGG

Answer 1

Răspuns:

Explicație pas cu pas:

a) (2⁴ - 4²)¹⁰⁰ = (16-16)¹⁰⁰ = 0¹⁰⁰ = 0

b) (5⁷:25²-11²)¹⁰:8⁶ = [5⁷:(5²)² - 121]¹⁰:(2³)⁶= [5⁷:5⁴-121]¹⁰:2³ˣ⁶ =

= (5⁷⁻⁴-121)¹⁰:2¹⁸ = (125-121)¹⁰ :2¹⁸ = 4¹⁰:2¹⁸ = (2²)¹⁰ :2¹⁸ = 2²⁰⁻¹⁸ = 2² = 4

c) (1¹⁰⁰-100⁰+3¹⁰⁰):(9^7²) = (1-1+3¹⁰⁰):(3²)⁴⁹ = 3¹⁰⁰:3⁹⁸ = 3¹⁰⁰⁻⁹⁸=3² = 9

d) (16⁴·8⁵:4¹⁵+2⁰+2²)·4-5² = [(2⁴)⁴·(2³)⁵:(2²)¹⁵+1+4)]·4-25 =

= (2¹⁶·2¹⁵:2³⁰+5)·4-25 = (2¹⁶⁺¹⁵⁻³⁰+5)·4-25 = 7·4-25 = 28-25 = 3

e) (1⁰+1¹+1²+1³+.....+1¹⁰²)⁵ : 103³ = [(1+1+1+.....+1)de103 ori]⁵ : 103³=

= 103⁵:103³ = 103⁵⁻³ = 103² = 10609

f) (3¹⁵+9⁷):3¹⁴ = [3¹⁵+(3²)⁷]:3¹⁴ = (3¹⁵+3¹⁴):3¹⁴ = 3¹⁴·(3+1):3¹⁴ = 4

g) (5¹²+25⁶+125⁴):5¹¹ = [5¹²+(5²)⁶+(5³)⁴]:5¹¹ =

= (5¹²+5¹²+5¹²):5¹¹ = 3·5¹²:5¹¹ = 3·5 = 15

h) (2²⁷:4⁶ +25⁴·2):(4⁷+5⁸) = [2²⁷:(2²)⁶ +(5²)⁴·2]:[(2²)⁷+5⁸] =

= [2²⁷:2¹²+2·5⁸]:[2¹⁴+5⁸] = (2²⁷⁻¹²+2·5⁸):(2¹⁴+5⁸) =

= (2¹⁵+2·5⁸):(2¹⁴+5⁸) =2·(2¹⁴+5⁸):(2¹⁴+5⁸) = 2

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