Zadanie 1
Zapisz w postaci potęgi liczby 6.
a)
[tex]( {6}^{4} {)}^{5} = [/tex]
b)
[tex] {6}^{4} \times {6}^{5} = [/tex]
c)
[tex] \frac{ {6}^{10} }{ {6}^{4} } = [/tex]
d)
[tex] {6}^{5} \div {6}^{4} = [/tex]
e)
[tex] {12}^{4} \times 0. {5}^{4} = [/tex]
f)
[tex] \frac{ {12}^{5} }{ {2}^{5} } = [/tex]

Zadanie 3
a)
[tex] {5}^{2} \times 25 = [/tex]
b)
[tex]125 \times {5}^{6} = [/tex]
c)
[tex] \frac{12 {5}^{8} }{5} = [/tex]
d)
[tex] {5}^{18} \div 2 {5}^{6} = [/tex]
e)
[tex]( {5}^{7} \times 25 {)}^{2} = [/tex]
f)
[tex] {25}^{10} \div {125}^{5} = [/tex]
g)
[tex] {(125}^{2} {)}^{5} \times 5 = [/tex]
h)
[tex]( \frac{ {5}^{9} }{125} {)}^{4} = [/tex]














Odpowiedź :

Odpowiedź:

1.

a)

(6^4)^5 = 6^20

b)

6^4 * 6^5 = 6^9

c)

6^10/6^4 = 6^6

d)

6^5 : 6^4 = 6

e)

12^4 * 0,5^4 = (12 * 0,5)^4 = 6^4f)

12^5 : 2^5 = (12/2)^5 = 6^5

3.

a)

5² * 25 = 5² * 5² = 5^4

b)

125 * 5^6 = 5³ * 5^6 = 5^9

c)

125^8/5 = (5³)^8 : 5 = 5 ^24 : 5 = 5^23

d)

5^18 : 25^6 = 5^18 : (5²)^6 = 5^18 : 5^12 = 5^6

e)

(5^7 * 25)² = 5^14 * (5²)² = 5^14 * 5^4 = 5^18

f)

25^10 : 125^5 = (5²)^10 : (5³)^5 = 5^20 : 5^15 = 5^5

g)

(125²)^5 * 5 = [(5³)²]^5 * 5 = (5^6)^5 * 5 = 5^30 * 5 = 5^31

h)

(5^9/125)^4 = 5^36 : (5³)^4 = 5^36 : 5^12 = 5^24

Szczegółowe wyjaśnienie: