Question

what is the exponent of 3 in 100! (!=factorial sign)

#ntse-preparation

Answer 1

Hey there! 

We know that 

Exponent of p in n! is p/n + p /n²+p/n³ + ... + p/n^k

here p =3, n = 100. 

So exponent or highest power of 3 in 100! is 100/3+ 100/3^2 + 100/3^3 +100/3^4 

= 33+11+3+1

= 48. 

Therefore, the exponent of 3 in 100! is 48

Answer 2

The exponent of 3 in 100! is 10.

Step-by-step explanation:

To find : What is the exponent of 3 in 100! ?

Solution :

We know,

$n!=n\times (n-1)\times (n-2).....$

So, 100! is written as

$100!=100\times 99\times 98\times 97\times 96\times 95......5!\times 4!\times 3!\times 2!\times 1!$

The factors of 3 among the terms are 3,9,27,81

i.e. $3^1,3^2,3^3,3^4$

The total power of exponent is $3^{1+2+3+4}=3^{10}$

Therefore, the exponent of 3 in 100! is 10.

#Learn more

Factorial

https://brainly.in/question/6107311, Answered by ChetnaNchauhan