Math Tutor Explains: What is 85 to the Power of 100?

A math tutor would explain that to solve for 85 to the power of 100, we must first understand the structure. The number 85 is called the base, and the number 100 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: 85 to the Power of 100 is equal to 8747673630108612022881490798938801709669643662874267258275330376308275153815318580662600057032598230796123573050817778749618310207945945073180669420060719121412518006764003075659275054931640625

Methods

Step-by-step from math tutor: finding 85 to the power of 100

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:

8510085^{100}

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

85 x 85 x 85 x 85 x ... (for a total of 100 times) = 8747673630108612022881490798938801709669643662874267258275330376308275153815318580662600057032598230796123573050817778749618310207945945073180669420060719121412518006764003075659275054931640625

Therefore, 85 to the power of 100 is 8747673630108612022881490798938801709669643662874267258275330376308275153815318580662600057032598230796123573050817778749618310207945945073180669420060719121412518006764003075659275054931640625.

Math Tutor Suggests: Try related exponent problems

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

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