5^400 or 4500 which is greater?
Trying to calculate 5^400 on my calculator caused it to hemorrhage , that's how huge the answer would be
If the question is about 5^400 and 4^500, then
5^400 = 10^(400*log5) = 10^279
4^500 = 10^(500*log4) = 10^301
so, 4^500 is 10^22 times as big as 5^400
To determine which is greater between 5^400 and 4500, we can compare the values directly.
First, let's calculate 5^400. The symbol "^" denotes exponentiation, so 5^400 means multiplying 5 by itself 400 times.
However, calculating 5^400 directly would be a very time-consuming process, as it involves multiplying 5 by itself 400 times. Instead, we can use the following approach:
1. Recognize that 5 = 5^1.
2. Observe that when multiplying two numbers with the same base, we add their exponents.
For example, 5^2 * 5^3 = (5 * 5) * (5 * 5 * 5) = 5^5.
3. Utilize the exponentiation property to simplify the calculation:
5^400 = (5^4)^100 = 625^100.
Now, let's compare 625^100 (which is equivalent to 5^400) and 4500.
Calculating 625^100 is still laborious, but we can make a simple comparison: 625^2 = 390,625. Therefore, 625^100 must be an enormous number because it involves multiplying 625 by itself 100 times.
In contrast, 4500 is a much smaller number.
Therefore, 5^400 (or 625^100) is significantly greater than 4500.