Math Tutor Explains: What is 85 to the Power of 65?

A math tutor would explain that to solve for 85 to the power of 65, we must first understand the structure. The number 85 is called the base, and the number 65 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 65 is equal to 258362912363671656128419536646602538678248864084578751943164288857836704955087172024159880567850677834940142929553985595703125

Methods

Step-by-step from math tutor: finding 85 to the power of 65

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:

856585^{65}

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

85 x 85 x 85 x 85 x ... (for a total of 65 times) = 258362912363671656128419536646602538678248864084578751943164288857836704955087172024159880567850677834940142929553985595703125

Therefore, 85 to the power of 65 is 258362912363671656128419536646602538678248864084578751943164288857836704955087172024159880567850677834940142929553985595703125.

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