Large exponents and standard numerals

Question

How many digits are in the standard numeral for

2^31 x 5^27

I was able to use an on line calculator and found the answer is 29.

My question is, how can I figure this out without the aid of a calculator able to handle such large numbers?

Answer 1

For solving this problem we will use the exponent product rule, to decompose 2³¹ _into 2⁴ x 2²⁷

So 2³¹ x 5²⁷ = 2⁴ x 2²⁷ x 5²⁷

Then we can make an exponent multiplication, we multiply the bases and keep the exponent.

2⁴ x 2²⁷ x 5²⁷ = 2⁴ x 10²⁷ = 16 x 10²⁷

10²⁷ is 1 followed by 27 zeros, and when multiplied by 16, you get 16 followed by 27 zeros, which makes a total of 29 digits.