Question

Proszę o pomoc ! Pilnie ! Daje naj i sporo pkt.

a.

b.

c.

d.

e.

f.

g.

z góry b. dziękuję !

Answer 1

a)

27⁵⁰ ÷ 81³⁷ = (3³)⁵⁰÷(3⁴)³⁷ = 3¹⁵⁰÷3¹⁴⁸ = 3¹⁵⁰⁻¹⁴⁸ = 3² = 9

b)

16⁷⁵ ÷ 64⁴⁹ = (4²)⁷⁵÷(4³)⁴⁹ = 4¹⁵⁰÷4¹⁴⁷ = 4³ = 64

c)

4·5³·5⁶ - 2·5⁴·5⁵          2(4·5⁹ - 2·5⁹)            8·5⁹ - 4·5⁹          5⁹(8-4)

--------------------   =   -------------------   =   ---------------   =   -------------   =  4

     ½·5²·5⁷                       5⁹                          5⁹                     5⁹

 

d)

⁴√81 = 3 

e)

⁴√256 = 4 

f)

¹⁰√1024 = 2 

g)

√128

-------   =   √(128/2) = √64 = 8

  √2

Answer 2

a) ... = (3^3)^50 : (3^4)^37 = 3^150 : 3^148 = 3^(150 - 148) = 3^2 = 9

b) .... = (4^2)^75 : (4^3)^49 = 4^150 : 4^147 = 4^(150 - 147) = 4^3 = 64

c) .... = (4 * 5^(3 + 6) - 2 * 5^(4 + 5)) / (1/2 * 5^(2 + 7)) = (4 * 5^9 -  2 * 5^9) / (1/2 * 5^9) = 2 * 5^9 / (1/2 * 5^9) = 2 / (1/2) = 2 : 1/2 = 2 * 2 = 4

d) .. = ⁴√(3*3*3*3) = 3

e) ... =⁴√256 = ⁴√(4 * 4 * 4 * 4) = 4

f) ... = ¹⁰√1024 = ¹⁰√(2^10) = 2^(10/10) = 2^1 = 2

g) ... = √128 / √2 = √(64 * 2) / √2 = 8√2/√2 = 8