Math Tutor Explains: What is 31 to the Power of 95?

A math tutor would explain that to solve for 31 to the power of 95, we must first understand the structure. The number 31 is called the base, and the number 95 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 95 is equal to 4779262825141566929692917638459126913375301280523729410955999402528459514164792807141078521123240335574442933654669002983141917972971439376351

Methods

Step-by-step from math tutor: finding 31 to the power of 95

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:

319531^{95}

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

31 x 31 x 31 x 31 x ... (for a total of 95 times) = 4779262825141566929692917638459126913375301280523729410955999402528459514164792807141078521123240335574442933654669002983141917972971439376351

Therefore, 31 to the power of 95 is 4779262825141566929692917638459126913375301280523729410955999402528459514164792807141078521123240335574442933654669002983141917972971439376351.

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