Math Tutor Explains: What is 31 to the Power of 99?

A math tutor would explain that to solve for 31 to the power of 99, we must first understand the structure. The number 31 is called the base, and the number 99 is called the exponent. In short, the base must be multiplied by itself the number of times as the exponent. Let’s look at this problem in more detail.

Math Tutor's Solution: 31 to the Power of 99 is equal to 4413749583537565032476932990387411346167271613890555109335495524222485458980983618043735976906256037950045112531693572303994207228316556664287051871

Methods

Step-by-step from math tutor: finding 31 to the power of 99

The first step a math tutor would suggest is to understand what it means when a number has an exponent. The “power” of a number indicates how many times the base would be multiplied by itself to reach the correct value.

The second step is to write the number in the base-exponent form, and lastly calculate what the final result would be. Consider the example of 2 to the power of 4: in exponent form that would be

242^4
. To solve this, we need to multiply the base, 2 by itself, 4 times -
2⋅2⋅2⋅22\cdot2\cdot2\cdot2
= 16. So
24=162^4 = 16
.

So re-applying these steps to our particular problem, we first convert our word problem to a base-exponent form of:

319931^{99}

To simplify this, all that is needed is to multiply it out:

31 x 31 x 31 x 31 x ... (for a total of 99 times) = 4413749583537565032476932990387411346167271613890555109335495524222485458980983618043735976906256037950045112531693572303994207228316556664287051871

Therefore, 31 to the power of 99 is 4413749583537565032476932990387411346167271613890555109335495524222485458980983618043735976906256037950045112531693572303994207228316556664287051871.

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