Math Tutor Explains: What is 75 to the Power of 92?

A math tutor would explain that to solve for 75 to the power of 92, we must first understand the structure. The number 75 is called the base, and the number 92 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: 75 to the Power of 92 is equal to 32035848562896240505190633614354504376938535140289246500766317922924584776105861211044517266449482678876403507531276808504596453398317879024403964649536646902561187744140625

Methods

Step-by-step from math tutor: finding 75 to the power of 92

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:

759275^{92}

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

75 x 75 x 75 x 75 x ... (for a total of 92 times) = 32035848562896240505190633614354504376938535140289246500766317922924584776105861211044517266449482678876403507531276808504596453398317879024403964649536646902561187744140625

Therefore, 75 to the power of 92 is 32035848562896240505190633614354504376938535140289246500766317922924584776105861211044517266449482678876403507531276808504596453398317879024403964649536646902561187744140625.

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