Math Tutor Explains: What is 47 to the Power of 76?

A math tutor would explain that to solve for 47 to the power of 76, we must first understand the structure. The number 47 is called the base, and the number 76 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: 47 to the Power of 76 is equal to 12007074439621798583106310800617106589152736015451686118433827019101784974777070512981913623888579673417702959220013029518992321

Methods

Step-by-step from math tutor: finding 47 to the power of 76

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:

477647^{76}

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

47 x 47 x 47 x 47 x ... (for a total of 76 times) = 12007074439621798583106310800617106589152736015451686118433827019101784974777070512981913623888579673417702959220013029518992321

Therefore, 47 to the power of 76 is 12007074439621798583106310800617106589152736015451686118433827019101784974777070512981913623888579673417702959220013029518992321.

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