Math Tutor Explains: What is 77 to the Power of 85?

A math tutor would explain that to solve for 77 to the power of 85, we must first understand the structure. The number 77 is called the base, and the number 85 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: 77 to the Power of 85 is equal to 22475617872138202716609477822157566244621591601947592572638832907122637213709566874906902691018906140635595861310665031264152769068584683838048645297078783777757

Methods

Step-by-step from math tutor: finding 77 to the power of 85

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:

778577^{85}

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

77 x 77 x 77 x 77 x ... (for a total of 85 times) = 22475617872138202716609477822157566244621591601947592572638832907122637213709566874906902691018906140635595861310665031264152769068584683838048645297078783777757

Therefore, 77 to the power of 85 is 22475617872138202716609477822157566244621591601947592572638832907122637213709566874906902691018906140635595861310665031264152769068584683838048645297078783777757.

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