Math Tutor Explains: What is 83 to the Power of 51?

A math tutor would explain that to solve for 83 to the power of 51, we must first understand the structure. The number 83 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: 83 to the Power of 51 is equal to 74641904363802797266214264251282814828210937723598580648775167654622860253966874545947033752606667

Methods

Step-by-step from math tutor: finding 83 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:

835183^{51}

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

83 x 83 x 83 x 83 x ... (for a total of 51 times) = 74641904363802797266214264251282814828210937723598580648775167654622860253966874545947033752606667

Therefore, 83 to the power of 51 is 74641904363802797266214264251282814828210937723598580648775167654622860253966874545947033752606667.

Math Tutor Suggests: Try related exponent problems

Our math tutors suggest reviewing other exponent problems that you can practice with!

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