Răspuns:
7) 1
8) 24
9) [tex]2^{1035}[/tex]
10) 1
Explicație pas cu pas:
7) [tex]125^{42}[/tex] ÷ [tex]25^{63}[/tex] =
[tex](5^{3})^{42}[/tex] ÷ [tex](5^{2})^{63}[/tex] =
[tex]5^{126}[/tex] ÷ [tex]5^{126}[/tex] = 1
8) ([tex]8^{37}[/tex] × [tex]81^{25}[/tex]) ÷ ([tex]16^{27}[/tex] × [tex]33^{27}[/tex]) =
[tex]\frac{8^{37}*81^{25}}{16^{27}*27^{33}}[/tex] =
[tex]\frac{2^{111}*3^{100}}{2^{108}*3^{99}}[/tex] =
[tex]2^{3} * 3[/tex] =
8 * 3 = 24
9) [tex]2^{1} *2^{2}*2^{3}*2^{4}*...*2^{45}[/tex]
[tex]2^{1+2+3+4+...+45)[/tex] =
[tex]2^{45+46 : 2}[/tex] =
[tex]2^{(45*23)}[/tex] = [tex]2^{1035}[/tex]
10) [tex](1+5^{10}) : (1+5^{10})[/tex] = 1
