Massive numbers can be represented using the exponent notation. For example, 3^100 is 3 raised to the power of 100. 3 is the base and 100 is the exponent.
Suppose we want to compare two massive numbers. Instead of computing the exact value of each number we can rely on a useful mathematical trick. Suppose m = a^b and n = c^d are two massive numbers. Let R be a relationship operator: less, equal or greater. Then we have the following:
If b*Log(a) R d*Log(c) then it is also the case that m R n,
where a, b, c, d, m and n are defined above.
So which is greater: 3^100 or 2^150? Let's do the math. 100*Log(3) = 47.7..., 150*Log(2) = 45.2.... Since 47.7 > 45.2, our rule tells us that 3^100 > 2^150.
Given two numbers **numberA** and **numberB** return the larger number formatted exactly the same as the input. **numberA** and **numberB** will be formatted as <base>^<exponent>. Constraints will ensure that **numberA** and **numberB** are not equal. |