Question

Przekształć i przedstaw w postaci jednej potęgi

a) 2^5*4^3*8

b) 2^5*4*3*8

c) 9^4*(8^2)^3:16^5

d) (25^3)^2:5^7*125^4

e) (64^4:32^4)^5*4^2:(16*8)

f) (27*81)^3:(9^4)^2

g) (32*2^8):8^3/128^2:32^2

h) (243^2:9^3)^2*(3^4)^3/24^2*81

^ - potęga

/ - kreska ułamkowa

Answer 1

a) 2^5 * 4^3 * 8  = 2^5 * (2^2)^3 * 2^3 =  2^5 * 2^6 * 2^3 = 2^14

 b) 2^5 * 4 * 3 * 8  =  2^5 * 2^2 * 3 * 2^3 = 3 * 2^10

 c) 9^4 * (8^2)^3 :16^5  =(3^2)^4 * (2^3)^6 : (2^4)^5 =

3^8 * 2^18 : 2^20 = 3^8 * 2^(-2)

 d) (25^3)^2 : 5^7 * 125^4=(5^2)^6 : 5^7 * (5^3)^4=

5^12 : 5^7 * 5^12 =5^5 * 5^12 = 5^17

 e) (64^4 : 32^4)^5 * 4^2 : (16 * 8) =

((2^6)^4 : (2^5)^4)^5 * (2^2)^2 : (2^4 * 2^3) = 

(2^24 : 2^20)^5 * 2^4 : 2^7 = (2^4)^5 * 2^4 : 2^7 =

2^20 * 2^4 : 2^7 = 2^24 : 2^7 = 2^15

 f) (27*81)^3:(9^4)^2  = (3^3 * 3^4)^3 : (3^2)^8 = (3^7)^3 : 3^16 = 3^21 : 3^16 = 3^5

 g) (32*2^8):8^3/128^2:32^2  =

(2^5 * 2^8) : (2^3)^3 / (2^7)^2 : (2^5)^2) = 

2^13  : 2^9 / 2^14 : 2^10 = 2^4 / 2^4 = 1

h) (243^2:9^3)^2*(3^4)^3/24^2*81 = 

(243^2 : 27^2)^2 * 3^12 / (24^2 * 9^2) =

[(243 : 27)^2 ] ^2  * 3^12 / (24 : 9)^2 = 

(9^2)^2 *  3^12 / (24 : 9)^2 = 

(3^2)^4 * 3^12 / (24 : 9)^2 =

3^8 * 3^12 / (24 : 9)^2 =

3^20 / (24 : 9)^2 = (3^10)^2 / (24 : 9)^2 = [ 3^10 / (24 : 9) ] ^2 = {3^10 * 9/24}^2 = (3^12/24)^2 = (3^11 / 8)^2