Math Tutor Explains: What is 83 to the Power of 56?

A math tutor would explain that to solve for 83 to the power of 56, we must first understand the structure. The number 83 is called the base, and the number 56 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 56 is equal to 294017494959938276468707277632144972495765946670396709392638693560698433377284820812167536876810468505766881

Methods

Step-by-step from math tutor: finding 83 to the power of 56

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:

835683^{56}

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

83 x 83 x 83 x 83 x ... (for a total of 56 times) = 294017494959938276468707277632144972495765946670396709392638693560698433377284820812167536876810468505766881

Therefore, 83 to the power of 56 is 294017494959938276468707277632144972495765946670396709392638693560698433377284820812167536876810468505766881.

Math Tutor Suggests: Try related exponent problems

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