12514488 were expressed as an integer, how many consecutive zeros would that integer have Ammediately to the left of its decimal point? (A) 22 (B) 32 (C) 42 (D) 50 (E) 112
Accepted Solution
A:
Answer: (B) 32Step-by-step explanation:Given expression : [tex]125^{14}48^{8}[/tex]Since, [tex]5^3=125[/tex] and [tex]48=16\times3=(2)^4\times3[/tex]Now, the given expression can be written as :[tex](5^3)^{14}((2)^4\times3)^{8}[/tex]Since, [tex](a^n)^m=a^{nm}[/tex]Then, [tex](5^3)^{14}((2)^4\times3)^{8}=5^{3\times14}(2^{4\times8}\times3^8)\\\\=5^{42}\times2^{32}\times3^8[/tex]Since, 10 is divisible by 5 and 2 but not 3. The greatest common number of values of 5 and 2 = 32Then, the number of consecutive zeros would that integer have immediately to the left of its decimal point =32