Question

Sum of the digits in the equation (16^100)*(125^135) is

Answer 1

Consider the given equation $16^{100}*125^{135}$

= $(2^{4 \times 100})*(5^{3 \times 135})$

=$(2^{400})*(5^{405})$

= $(2^{400})*(5^{400}*5^{5})$

=$[(2 \times 5)^{400}]*(5^{5})$

= $(10^{400})*(3125)$

Since $10^n = 10000000...$

= $312500000....$

So, the sum of the digits = 3+1+2+5+0+0+0+0+......+0

= 11.

So, the sum of the digits in the given expression is 11.

Answer 2

Let us take the given number and factorize it in a simple form

(16^100} * (125^135}  

=  (2^{4 * 100}) * (5^{3 * 135})  

= (2^400) * (5^405)  

=  (2^{400}) * (5^{400}*5^{5})  

= [(2 * 5)^{400}] * (5^{5})  

=  (10^{400}) * (3125)  

Since  10^n = 10000000............ ( n times) , so the given term will be of the form  312500000  ( 400 times) and from this number we can find the sum of the digits

So, the sum of the digits = 3+1+2+5+0+0+0+0+......+0 (400 times zero)

                                          = 11.

Answer: the sum of the digits in the given expression is 11.