Math Tutor Explains: What is 78 to the Power of 75?

A math tutor would explain that to solve for 78 to the power of 75, we must first understand the structure. The number 78 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: 78 to the Power of 75 is equal to 8074120038085312594064984448503882120710763073157663464332483983147657548899675017715550839940216679911020516171923552334280822699663065874432

Methods

Step-by-step from math tutor: finding 78 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:

787578^{75}

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

78 x 78 x 78 x 78 x ... (for a total of 75 times) = 8074120038085312594064984448503882120710763073157663464332483983147657548899675017715550839940216679911020516171923552334280822699663065874432

Therefore, 78 to the power of 75 is 8074120038085312594064984448503882120710763073157663464332483983147657548899675017715550839940216679911020516171923552334280822699663065874432.

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