Réponse :
Explications étape par étape
(a/b)^n = a^n/b^n
a^n/a^(-n) = a^(n+n) = a^(2n)
a^n/a^p = a^(n-p)
(a/b)^(-n) = (b/a)^n
Bonjour
A = (2/3)^5 x (3/2)^(-7) x (2/3)^(-4) x (3/2)^(-6)
A = (2/3)^5 x (2/3)^7 x (3/2)^4 x (2/3)^6
A = (2/3)^(5+7+6) x (3/2)^4
A = (2/3)^18 x (3/2)^4
A = 2^18 x 3^(-18) x 3^4 x 2^(-4)
A = 2^(18-4) x 3^(4-18)
A = 2^14 x 3^(-14)
A = (2/3)^14
B = (2^3)^(-5) x 8^4 x 4^2
B = 2^(3*(-5)) x (2^3)^4 x (2^2)^2
B = 2^(-15) x 2^(3*4) x 2^(2*2)
B = 2^(-15) x 2^12 x 2^4
B = 2^(-15+12+4)
B = 2^1
B = 2
C = [(5^3 x 7^(-1))/(3 x 2^(-2))]^(-2) x (25^3 x 9^(-1))/(49 x 16^(-1))
C = 5^(3*(-2)) x 7^(-1*(-2)) x 3^(-1*(-2)) x 2^(2*(-2)) x (5^2)^3 x 9^(-1) x 7^(-2) x (4^2)
C = 5^(-6) x 7^2 x 3^2 x 2^(-4) x 5^(2*3) x (3^2)^(-1) x 7^(-2) x (2^2)^2
C = 5^(-6) x 7^2 x 3^2 x 2^(-4) x 5^6 x 3^(-2) x 7^(-2) x 2^4
C = 5^(6-6) x 7^(2-2) x 3^(2-2) x 2^(4-4)
C = 5^0 x 7^0 x 3^0 x 2^0
C = 1 x 1 x 1 x 1
C = 1
D = (2^3 - 3^2)^2019 + (5^2 - 3^3)^3
D = 2^(3*2019) - 3^(2*2019) + 5^(2*3) - 3^(3*3)
D = 2^6057 - 3^4038 + 5^6 - 3^9
D = 2^6057 - 3^4038 - 3^9 + 5^6
