Question

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Exercițiile 1 și 2







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Answer 1

1. a) 2^5

b) 2^7

c) 2^9

d) (2^2)^35=2^70

e) (2^4)^7=2^28

f) 2^10

2. a) 31

b) 81-64=17

c) 125+243=368

d) 32-25=7

e) 128+49=177

f) 81-81=0

g) 8+4+2+1=12+3=15

h) 3^9-(3^3)^3=3^9-3^9=0 

Answer 2

1)

a) 32 = 4 × 8 = 2² × 2³ = 2⁽ ² ⁺ ³⁾ = 2⁵

b) 128 = 4 x 32 = 4 x 4 x 8 = 2² x 2² x 2³ = 2 ⁽² ⁺ ² ⁺ ³ ⁾ = 2⁷

c) 512 = 4 x 128 = 2² x 2⁷ = 2²⁺⁷ = 2⁹

d) 4³⁵ = ( 2²) ³⁵ = 2 ⁽² ˣ ³⁵ ⁾ = 2⁷⁰

e) 16⁷ = ( 2⁴)⁷ = 2 ⁽ ⁴ ˣ ⁷ ⁾ = 2 ²⁸

f) 1 024 = 4 x 256 = 4 x 4 x 64 = 2 ²x 2² x 8 x 8 = 2 ⁴ x 2³x 2³ = 2 ⁽⁴ ⁺ ³ ⁺ ³⁾ = 2¹⁰

2)

2² + 3³ = 4 + 27 = 31

b) 3⁴ - 4³ = 81 - ( 16 x 4 ) = 81 - 64 = 17

c) 5³ + 3⁵ = ( 25 x 5 ) + 243 = 125 + 243 = 368

d) 2⁵ - 5² = 32 - 25 = 7

e) 2⁷ + 7² = 128 + 49 = 177

f) 3⁴ - 9² = 0 ( 81 - 81 = 0)

g) 2³ + 2² + 2¹ + 2⁰ = 8 + 4 + 2 + 1 = 15

h) 3⁹ - 27³ = 3⁹ - ( 3³)³ = 3⁹ - 3⁹ = 0