Answer: (B) 32
Step-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 = 32
Then, the number of consecutive zeros would that integer have immediately to the left of its decimal point =32
