L'exercice SC3:
[tex]A=a^3 \times b^4 \times a^7 \times (b^2)^{-4}\\.\ \ =a^3 \times a^7 \times b^4 \times b^{2*(-4)}\\.\ \ =a^{3+7} \times b^4 \times b^{-8}\\.\ \ =a^{10} \times b^{4+(-8)}\\A=a^{10} \times b^{-4}=\frac{a^{10}}{b^4}\\\\B= 2^4 \times 5^{-3} \times 16 \times 5^7\\=2^4 \times 5^{-3} \times 2^4 \times 5^7\\=2^{4+4} \times 5^{-3+7}\\B=2^8 \times 5^4\\[/tex]
[tex]C=\frac{a^{-1} \times a^4 \times b^{-2}}{b^2 \times a^1}\\\\=a^{-1+4-(1)} \times b^{-2-(2)}\\\\C=a^2 \times b^{-4}=\frac{a^2}{b^4}\\D=\frac{a^3 \times b^{-1} \times a^2}{(a^2)^3 \times (b^{-1})^{-2}}\\\\=a^{3+2-2*3} \times b^{-1-(-1)*(-2)}\\=a^{-1} \times b^{-3}\\D=\frac{1}{a\ b^3}\\[/tex]
L'exercices 73 et 74: factoriser:
[tex]A=2^{10} - 2^9 = 2^{1+9} - 2^9=2^1 \times 2^9 - 2^9\\=(2-1)2^9=2^9=2*2*2*2*2*2*2*2*2\\[/tex]
[tex]B=3^{20}-3^{21}=1 \times 3^{20}-3^1 \times 3^{20}\\=(1-3)*(3^{20})=-2 \times 3^{20}\\[/tex]
[tex]C=5^{12}+5^{11}=5^{11} \times (5+1)=6 \times 5^{11}\\=2 \times 3 \times 5^{11}\\[/tex]
[tex]D=7^{31}+7^{29}=7^{29} \times 7^2 + 7^{29} \times 1\\=7^{29} \times (7^2 + 1)\\=7^{29} \times 50\\=7^{29} \times 5^2 \times 2\\[/tex]
