Réponse :
Explications étape par étape
Bonjour
Forme Fractionnaire :
A = (5^4 x 6^3 x 2^4 x 8^5)/(10^4 x 2^25 x 3^5)
A = (5^4 x (2 x 3)^3 x 2^4 x (2^3)^5)/((2 x 5)^4 x 2^25 x 3^5)
A = (5^4 x 2^3 x 3^3 x 2^4 x 2^15)/(2^4 x 5^4 x 2^25 x 3^5)
A = 5^(4-4) x 2^(3+4+15-4-25) x 3^(3-5)
A = 5^0 x 2^(-7) x 3^(-2)
A = 1/(2^7 x 3^2)
A = 1/(128 x 27)
A = 1/3456
Forme à x 2^n :
B = (8^3 x 10^4 x 9^3 x 7^3)/(5^4 x 6^4 x 21^3)
B = [(2^3)^3 x 2^4 x 5^4 x (3^2)^3 x 7^3]/[5^4 x 2^4 x 3^4 x 3^3 x 7^3]
B = 2^9 x 2^4 x 5^4 x 3^6 x 7^3 x 5^(-4) x 2^(-4) x 3^(-4) x 3^(-3) x 7^(-3)
B = 2^(9+4-4) x 3^(6-4-3) x 5^(4-4) x 7^(3-3)
B = 2^9 x 3^(-1)
B = 1/3 x 2^9
Écriture scientifique :
C = (0,3 x 5^6 x 5,1 x 8^2)/(3,4 x 2^3 x 25^2)
C = (3/10 x 5^6 x 51/10 x (2^3)^2)/(34/10 x 2^3 x 5^2 x 5^2)
C = (3 x 5^6 x 3 x 17 x 2^6 x 10^(-2)) / (2 x 17 x 2^3 x 5^2 x 5^2 x 10^(-1))
C = 2^(6-1-3) x 3^(1+1) x 5^(6-2-2) x 17^(1-1) x 10^(-2+1)
C = 2^2 x 3^2 x 5^2 x 10^(-1)
C = 4 x 9 x 25 x 10^(-1)
C = 900 x 10^(-1)
C = 9 x 10^2 x 10^(-1)
C = 9 x 10^(2-1)
C = 9 x 10^1
Écriture décimale et scientifique :
D = (1,5^4 x 0,25 x 8,1^2)/(0,03 x 7,5 x 60)
D = (15/10)^4 x 25/100 x (81/10)^2 / [3/100 x 75/10 x 60]
D = (15^14 x 10^(-4) x 25 x 10^(-2) x 81^2 x 10^(-2) / [3 x 10^(-2) x 75 x 10^(-1) x 6 x 10]
D = 3^14 x 5^14 x 10^(-4) x 5^2 x 10^(-2) x (3^4)^2 x 10^(-2) x 3^(-1) x 10^2 x 5^(-2) x 3^(-1) x 10^(-1) x 2^(-1) x 3^(-2) x 10^(-1)
D = 3^(14+8-1-1-2) x 5^(14+2-2) x 10^(-4-2-2+2-1-1) x 2^(-1)
D = 3^18 x 5^14 x 10^(-8) x 2^(-1)
D = 3^18 x 5^14 x 2^(-8) x 5^(-8) x 2^(-1)
D = 3^18 x 5^(14-8) x 2^(-8-1)
D = 3^18 x 5^6 x 2^(-9)
D = 387 420 489 x 15 625 x 0,001 953 12
D = 11 823 135 040, 283 2
D = 1,182 313 504 028 32 x 10^10
