Question

Oblicz: a) 1,5 ^ 8 * (2/3)^8

b) 0,6 ^5 * (6 i 2/3) ^ 5

c)10000 * 0,2 ^ 4

d) 0,8 ^ 5 * 2,5 ^ 5

e) (5/7) ^3 / (2 i 1/7) ^ 3

f) 81 * 0,25 ^ 4 / 0,75 ^ 4

Answer 1

a)

1,5^8 * ( 2/3)^8 = ( 3/2)^8 *( 2/3)^8 = [ (3/3)*(2/3)]^8 = 1^8 = 1

wzór : a^n * b^n = ( a*b)^n

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b)

0,6^5 * ( 6  2/3)^5 = ( 6/10)^5 * ( 20/3)^5 = [ ( 6/10)*( 20/3)]^5 = 4^5 = 2^10 = 1024

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c)

10 000 * 0,2^4 = 10^4 * 0,2^4 = ( 10*0,2)^4 = 2^4 = 16

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d)

0,8^5 * 2,5^5 = ( 0,8 *2,5)^5 = 2^5 = 32

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e)

( 5/7)^ 3 / (2  1/7)^ 3 = ( 5/7)^3  / (15/7)^3 = [ ( 5/7)/(15/7)]^3 =

= [ ( 5/7)*(7/15)]^ 3 = ( 1/3)^3 = 1/27

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f)

81*0,25^ 4 / 0,75^4 = 81*[ 0,25/0.75)^4 = 81 *( 1/3)^4 = 81* ( 1/81) = 1

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Answer 2

a) = (1 1/2)^8 * (2/3)^8 = (3/2)^8 * (2/3)^8 = 1^8 = 1
b) = (6/10)^5 * (20/3)^5 = 4^5 = 1024

c) = 10^4 * 0,2^4 = 2^4 = 16

d) = 0,8^5 * 2,5^5 = 2^5 = 32

e) = (5/7)^3 * (7/15)^3 = (1/3)^3 = 1/27

f) = 3^4 * (1/4)^4 : (3/4)^4 = 3^4 * (1/4)^4 * (4/3)^4 = 1^4 = 1