Which quantity is larger?
a. 100^500
b. 1000^300
c. they are equal
d. insufficient information
I believe it is B but can someone check? Thanks!
1000 = 10^3, so
1000^300 = (10^3)^300 = 10^900
which is much bigger than 10^500
To figure out which quantity is larger, we need to compare the values of a. 100^500 and b. 1000^300.
We can solve this problem by understanding the properties of exponents. For the given question, the base number is different for both quantities, but the power/exponent is what really makes the difference.
Let's calculate the values:
a. 100^500 = 100 multiplied by itself 500 times
b. 1000^300 = 1000 multiplied by itself 300 times
Simplifying these calculations would be tricky given the large numbers involved. However, we can use a comparison method:
We know that 100^500 will be smaller than any value obtained by multiplying 1000^x by 1000^y (where x and y are positive integers) because the base number 1000 is greater than 100.
So, it is safe to conclude that b. 1000^300 is indeed larger than a. 100^500.
Therefore, the correct answer is b. 1000^300.
Keep in mind that using a calculator or a computer program would be the most effective way to calculate such large numbers.