Math Tutor Explains: What is 91 to the Power of 75?

A math tutor would explain that to solve for 91 to the power of 75, we must first understand the structure. The number 91 is called the base, and the number 75 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: 91 to the Power of 75 is equal to 847431150512427734532146130154656417595899021460622020385178827607312710349260580303949634633937343262207623680918623190017814292729921822483709251

Methods

Step-by-step from math tutor: finding 91 to the power of 75

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:

917591^{75}

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

91 x 91 x 91 x 91 x ... (for a total of 75 times) = 847431150512427734532146130154656417595899021460622020385178827607312710349260580303949634633937343262207623680918623190017814292729921822483709251

Therefore, 91 to the power of 75 is 847431150512427734532146130154656417595899021460622020385178827607312710349260580303949634633937343262207623680918623190017814292729921822483709251.

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