Réponse:
1.
[tex]1.( 8^2 \times 16^3 = (2^3)^2 \times (2^4)^3 = 2^{3 \times 2} \times 2^{4 \times 3} = 2^{6 + 12} = 2^{18} ).[/tex]
2.
[tex]( 25^2 \times 1.45 \times 4^2 = (5^2)^2 \times 1.45 \times (2^2)^2 = 5^{2 \times 2} \times 1.45 \times 2^{2 \times 2} = 5^4 \times 1.45 \times 2^4 ).( 5^4 \times 2^6 \times 4^{13} \times 5 \times 0.25^{11} = 5^4 \times (2^2)^3 \times (2^2)^{13} \times 5 \times (0.25^2)^5 = 5^4 \times 2^{2 \times 3} \times 2^{2 \times 13} \times 5 \times (0.25^2)^5 = 5^4 \times 2^{6 + 26} \times 5 \times 0.25^{10} ).( 2^3 \times 5^2 \times 2^2 \times 5^7 \times 2^2 = 2^{3 + 2} \times 5^{2 + 7} \times 2^2 = 2^5 \times 5^9 \times 2^2 ).( 9^3 \times 7^2 \times 8^5 \times 7^4 \times 0^2 \times 4^3 = 9^3 \times 7^6 \times 8^5 \times 4^3 ).[/tex]
3.
[tex]( -2^{16} ) : négatif( (-3)^{12} ) : positif( -2 \times (-3)^{15} ) : négatif( (-2)^{19} \times (-3)^{11} ) : positif[/tex]
4.
[tex]( 2^3 + 5^3 \times 2 + 5^3 = 8 + 125 \times 2 + 125 = 8 + 250 + 125 = 383 ).( (-2)^2 + 2 \times (-3)^3 - 2 - 3 \times (-2)^2 = 4 + 2 \times (-27) - 2 - 3 \times 4 = 4 - 54 - 2 - 12 = -64 ).( (-2) \times 3^2 - 3 \times (-2)^3 = -2 \times 9 - 3 \times (-8) = -18 + 24 = 6 ).[/tex]
