How to Compare Numbers With Large Exponents

An exponent is a mathematical symbol that represents how often a number is multiplied by itself. For example, 10^3 means that 10 should be multiplied by itself 3 times: 10 x 10 x 10; and 2^2 means that two should be multiplied by itself two times: 2 x 2. The exponent is commonly found as a superscript number to the right of a base. While calculators can evaluate larger exponents, like 9^67 or 5^24, they cannot easily evaluate very large exponents like 4^6879 or 11^29872.

Things You'll Need

• Calculator

Instructions

1. Compare the numbers without the exponents. If one number is a fraction and one is not, the fraction will always be smaller than the whole number, regardless of the size of the exponent. For example, .9^987392846749037937 is smaller than 10^1 and .23^19893475 is smaller than 9^2.

2. Put the numbers into the calculator. If your exponent isn't massive, the calculator will return scientific notation (a way of writing large numbers) that is easier to compare. For example, if you were comparing 2^309 and 9^356278, put 2^309 into the calculator to get 1.04296242 x 10^93 and 1.1^509 to get 1.17186274 x 10^21.

3. Compare the powers of ten. In the example, you have 10^93 and 10^21. 10^93 is clearly larger than 10^21.

Tips & Warnings

• For large exponents, you may need to find a powerful computer. Very large exponents can be impossible for even the most powerful handheld calculators to evaluate. For example, 10^8763 will cause most calculators (including graphing calculators) to return "infinity."