Question

A googol is the number 1 followed by 100 zeroes.

1. How is a googol written as a power?
2. How is a googol times a googol written as a power?

Answer 1

a. 1 googol = `ubrace(1000"_ _ _"0)_(100  "times")` = 1 × 10¹⁰⁰  ...[As there are 100 zeroes after 1]

b. Googol times googol means multiply googol by googol

∴ Required number = googol × googol = 10¹⁰⁰ × 10¹⁰⁰ ...[∵ 1 googol = 10¹⁰⁰]

= `10^(100 + 100)`  ...[∵ a^m × aⁿ = a^{m + n}]

= 100²⁰⁰