Math Tutor Explains: What is 32 to the Power of 85?

A math tutor would explain that to solve for 32 to the power of 85, we must first understand the structure. The number 32 is called the base, and the number 85 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: 32 to the Power of 85 is equal to 86645927941275464361825443254471365732388658605494267974077486894206915868925800719999200190754361815543475342543861619655442432

Methods

Step-by-step from math tutor: finding 32 to the power of 85

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:

328532^{85}

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

32 x 32 x 32 x 32 x ... (for a total of 85 times) = 86645927941275464361825443254471365732388658605494267974077486894206915868925800719999200190754361815543475342543861619655442432

Therefore, 32 to the power of 85 is 86645927941275464361825443254471365732388658605494267974077486894206915868925800719999200190754361815543475342543861619655442432.

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