Math Tutor Explains: What is 63 to the Power of 78?

A math tutor would explain that to solve for 63 to the power of 78, we must first understand the structure. The number 63 is called the base, and the number 78 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: 63 to the Power of 78 is equal to 223132513376098223485357705040354235632291532124000130576241525926609110047362751778655811709593592210226577921291463156434454137408972364929

Methods

Step-by-step from math tutor: finding 63 to the power of 78

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:

637863^{78}

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

63 x 63 x 63 x 63 x ... (for a total of 78 times) = 223132513376098223485357705040354235632291532124000130576241525926609110047362751778655811709593592210226577921291463156434454137408972364929

Therefore, 63 to the power of 78 is 223132513376098223485357705040354235632291532124000130576241525926609110047362751778655811709593592210226577921291463156434454137408972364929.

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