Question

If n =2^3*3^4*5^4*7 then the number of consecutive zeroes in n where n is a natural number is

Answer 1

2^3=8
3^4=81
5^4=625
2^3×3^4×5^4×7
=8×81×625×7
=2835000
there fore n= 3

Answer 2

We need to recall the following definition of an exponent.

An exponent is a power of a number.

If $b$ is the exponent of the base $a$, then $a$ is multiplied by itself $b$ times.

This problem is about the exponents.

Given:

$n=2^3*3^4*5^4*7$

$n=8*81*625*7$

$n=648*4375$

$n=2835000$

There are three zeroes present at the end of the number.

Thus, the number of consecutive zeroes in the $n=2835000$ is $3$.