Math Tutor Explains: What is 85 to the Power of 79?

A math tutor would explain that to solve for 85 to the power of 79, we must first understand the structure. The number 85 is called the base, and the number 79 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: 85 to the Power of 79 is equal to 265518711226513720899086722935111681216940076000376568848213909481110997497797896411686569047437684696400908329790013784332813884248025715351104736328125

Methods

Step-by-step from math tutor: finding 85 to the power of 79

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:

857985^{79}

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

85 x 85 x 85 x 85 x ... (for a total of 79 times) = 265518711226513720899086722935111681216940076000376568848213909481110997497797896411686569047437684696400908329790013784332813884248025715351104736328125

Therefore, 85 to the power of 79 is 265518711226513720899086722935111681216940076000376568848213909481110997497797896411686569047437684696400908329790013784332813884248025715351104736328125.

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