Math Tutor Explains: What is 75 to the Power of 82?

A math tutor would explain that to solve for 75 to the power of 82, we must first understand the structure. The number 75 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: 75 to the Power of 82 is equal to 5688838412621295582308044815797962502591525923091658950835330417508945012818164494780981174479590297801064147456030772875834600199596025049686431884765625

Methods

Step-by-step from math tutor: finding 75 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:

758275^{82}

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

75 x 75 x 75 x 75 x ... (for a total of 82 times) = 5688838412621295582308044815797962502591525923091658950835330417508945012818164494780981174479590297801064147456030772875834600199596025049686431884765625

Therefore, 75 to the power of 82 is 5688838412621295582308044815797962502591525923091658950835330417508945012818164494780981174479590297801064147456030772875834600199596025049686431884765625.

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