Math Tutor Explains: What is 97 to the Power of 82?

A math tutor would explain that to solve for 97 to the power of 82, we must first understand the structure. The number 97 is called the base, and the number 82 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: 97 to the Power of 82 is equal to 8227771268492461824223470023415396764101632020003744078537271697214992746852007778224562278255066021500050650606026835267125559141553949008347175475615114137903809

Methods

Step-by-step from math tutor: finding 97 to the power of 82

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:

978297^{82}

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

97 x 97 x 97 x 97 x ... (for a total of 82 times) = 8227771268492461824223470023415396764101632020003744078537271697214992746852007778224562278255066021500050650606026835267125559141553949008347175475615114137903809

Therefore, 97 to the power of 82 is 8227771268492461824223470023415396764101632020003744078537271697214992746852007778224562278255066021500050650606026835267125559141553949008347175475615114137903809.

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