Exercice 1 : Application des règles de base
A) \( A = 3^2 \times 3^4 \)
B) \( B = \frac{5^7}{5^3} \)
C) \( C = (7^2)^3 \)
D) \( D = 2^5 \times 5^5 \)
E) \( E = (10^5)^{-2} \)
Exercice 2 : Puissances négatives et fractions
A) \( A = 2^{-3} \)
B) \( B = \frac{1}{4^{-2}} \)
C) \( C = \left(\frac{2}{3}\right)^3 \)
D) \( D = \left(\frac{1}{5}\right)^{-2} \)
E) \( E = \frac{2^5}{2^9} \)
Exercice 3 : Expressions complexes
A) \( A = \frac{2^3 \times 2^{-4}}{2^5} \)
B) \( B = \frac{(3^4)^2 \times 3^{-5}}{3} \)
C) \( C = \left(\frac{2^2}{5}\right)^3 \times 5^4 \)
D) \( D = \frac{a^2 b^{-3} c^4}{a^5 b^{-1} c^2} \)
E) \( E = \frac{(-2)^4 \times 4^2}{8^3} \)
Exercice 4 : Écriture scientifique
A) \( A = 845 \, 000 \)
B) \( B = 0,00034 \)
C) \( C = 254 \times 10^3 \)
D) \( D = 0,025 \times 10^{-2} \)
E) \( E = \frac{1}{2000} \)
Exercice 5 : Calculs en notation scientifique
A) \( A = \frac{45 \times 10^{-5}}{5 \times 10^4} \)
B) \( B = \frac{2 \times 10^{-4} \times 1,2 \times 10^2}{3 \times 10^{-1}} \)
C) \( C = \frac{0,8 \times 10^{-6} \times 1,5 \times 10^8}{2 \times 10^3} \)
D) \( D = 5 \times 10^{-4} + 25 \times 10^{-5} \)
E) \( E = \frac{7 \times 10^5 \times 8 \times 10^{-2}}{2 \times 10^2} \)