What is the sum of the digits of the number $(5^{2015})(2^{2018})$
So I am guessing, I have to find out the product of $(5^{2015})(2^{2018})$ and add each digit of the product.
The question is how do I find the product of $(5^{2015})(2^{2018})$. Both numbers don't share the same base or exponents, so none of the laws of exponents (that I know of) will help me. Unless this problem is meant to be clever and have another way.
Any leads?
Best Answer
$$(5^{2015})(2^{2018}) = (5^{2015})(2^{2015})(2^3) = (5\cdot 2)^{2015}2^3$$ $$= 10^{2015}2^3 = 8\cdot 10^{2015}$$ Notice that this is just the digit $8$ followed by $2015$ zeroes, so the sum is just $8$