Math Tutor Explains: What is 86 to the Power of 51?

A math tutor would explain that to solve for 86 to the power of 51, we must first understand the structure. The number 86 is called the base, and the number 51 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: 86 to the Power of 51 is equal to 456479221261906596415896937894198532722420649086677434938847902628735718755127817489194589236494336

Methods

Step-by-step from math tutor: finding 86 to the power of 51

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:

865186^{51}

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

86 x 86 x 86 x 86 x ... (for a total of 51 times) = 456479221261906596415896937894198532722420649086677434938847902628735718755127817489194589236494336

Therefore, 86 to the power of 51 is 456479221261906596415896937894198532722420649086677434938847902628735718755127817489194589236494336.

Math Tutor Suggests: Try related exponent problems

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