Math Tutor Explains: What is 78 to the Power of 83?

A math tutor would explain that to solve for 78 to the power of 83, we must first understand the structure. The number 78 is called the base, and the number 83 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: 78 to the Power of 83 is equal to 11062467894801356137407860010980871110585039116612543830850552351475679217897980617427209171169791352653179392419664760930268366643661824808572926957035978752

Methods

Step-by-step from math tutor: finding 78 to the power of 83

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:

788378^{83}

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

78 x 78 x 78 x 78 x ... (for a total of 83 times) = 11062467894801356137407860010980871110585039116612543830850552351475679217897980617427209171169791352653179392419664760930268366643661824808572926957035978752

Therefore, 78 to the power of 83 is 11062467894801356137407860010980871110585039116612543830850552351475679217897980617427209171169791352653179392419664760930268366643661824808572926957035978752.

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