Question

Cate zerouri si cate cifre are nr 2^2nx2+5^2nx5^3

Answer 1

  
[tex](2^{2n} \times 2) \times (5^{2n} \times 5^3)= \\ =2^{2n}\times 2^1 \times 5^{2n} \times 5^{1+2}= \\ =2^{2n+1} \times 5^{2n} \times 5^1 \times 5^2}= \\ =2^{2n+1} \times 5^{2n+1} \times 5^2}= \\ =(2 \times 5)^{2n+1} \times 5^2}=10^{2n+1} \times 25}=25 \underbrace{00000000...0000}_{ 2n+1~zerouri} \\ \\ \texttt{Numarul este 25 urmat de 2n+1 zerouri.} \\ \Longrightarrow ~~ \texttt{Numarul are 2n+1~zerouri, si in total are 2n+3 cifre } [/tex]