Question

Rezultatul calculului (-125 la puterea 20) : 25 la puterea 30 este?

Answer 1

Faci asa:
     Trebuie sa desfaci toate numerele cu puteri folosind regulile: ($(x^{n} )^{m}=(x^{m} )^{n}=x^{n*m} \\ a=m*n=\ \textgreater \ x^{a}=x^{m*n}=(x^{m} )^{n}$
     Deci $-125^{20}=-(125^{2})^{10}$  si $25^{30}=(25^{3})^{10}$. 
    Impartite dau $\left \{ {{( \frac{-125^{2}}{25^{3}}) ^{10}} \atop {-125^{2}=-(5^{3})^{2}\atop{25^{3}=(5^{2})^{3}}}}\right.=\ \textgreater \ [ \frac{-(5^{3})^{2}}{(5^{2})^{3}} ]^{10}=[ \frac{(-5^{2})^{3}}{(5^{2})^{3}} ]^{10}=-1^{10}=-1$