Math Tutor Explains: What is 51 to the Power of 71?

A math tutor would explain that to solve for 51 to the power of 71, we must first understand the structure. The number 51 is called the base, and the number 71 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: 51 to the Power of 71 is equal to 17277563704993856532212363451596447596623771700684409630436173949266784426333262575344791804129467839402142422442056841051

Methods

Step-by-step from math tutor: finding 51 to the power of 71

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:

517151^{71}

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

51 x 51 x 51 x 51 x ... (for a total of 71 times) = 17277563704993856532212363451596447596623771700684409630436173949266784426333262575344791804129467839402142422442056841051

Therefore, 51 to the power of 71 is 17277563704993856532212363451596447596623771700684409630436173949266784426333262575344791804129467839402142422442056841051.

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