Question

(2^6)^5×{3^4 ×28-[3-(2^3×5^3-3^2×10^2-5^2):(1+4)^2]:10^4-2^2^0×3^4}>2^7×4^5×3^25

Answer 1

Răspuns:

Explicație pas cu pas:

2^2^0 = 2^1

( 2⁶)⁵x { 3⁴ x 28 - [ 3 - ( 2³ x 5³ - 3²x 10²- 5²): 5² ] : 10⁴- 2¹x 3⁴} =

= 2³⁰ x { 81 x 28 - [3 - (8x5 - 3²x 2²- 1 ) x 5² : 5²] : 10⁴ - 2 x 81} =

= 2³⁰ x { 81x 28 - [ 3 - ( 40 - 9x4 - 1) x 1 ] : 10⁴ - 2 x 81} =

= 2³⁰ x [ 81 x 28 - ( 3 - 3) : 10⁴ - 2 x 81] =

= 2³⁰ x ( 81 x 28 - 0 : 10⁴ - 2 x 81 ) =

= 2³⁰x 81 x ( 28 - 2) =

= 2³⁰ x 3⁴ x 26 =

= 2³⁰ x 3⁴ x 2 x 13

= 2³¹ x 3⁴ x 13

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SAU:

= 2⁶ˣ⁵ x { 81 x 28 - [ 3 - (10³ - 30² - 25 ) : 25 ] : 10⁴ - 2 x 81 } =

= 2³⁰ x { 2268 - [ 3 - ( 1000 - 900 - 25 ) : 25 ] : 10⁴- 162} =

= 2³⁰ x [ 2268 - ( 3 - 75 : 25 ) : 10⁴ - 162 ] =

= 2³⁰ x ( 2268 - 0 : 10⁴ - 162 ) =

= 2³⁰ x ( 2268 - 0 - 162 ) =

= 2³⁰ x 2106 =

= 2³⁰ x 2 x 3⁴ x 13

= 2³¹ x 3⁴ x 13  

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2⁷ x 4⁵ x 3²⁵ =

= 2⁷ x( 2²)⁵ x 3²⁵=

= 2⁽⁷⁺²ˣ⁵⁾ x 3²⁵ =

= 2¹⁷ x 3²⁵

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2³¹ x 3⁴ x 13  >  2¹⁷ x 3²⁵  fals

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2³¹ x 3⁴ x 13 cu  2¹⁷ x 3²⁵   l  :   2¹⁷ x 3⁴

2³¹⁻¹⁷ = 2¹⁴

2¹⁴ x 13  cu  3²¹ ( 3¹⁴ x 3⁷)

2¹⁴ x 13 <  3¹⁴ x 3⁷;  2 < 3, dar si 13 <  3⁷