Math Tutor Explains: What is 64 to the Power of 76?

A math tutor would explain that to solve for 64 to the power of 76, we must first understand the structure. The number 64 is called the base, and the number 76 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: 64 to the Power of 76 is equal to 186070713419675363980626894819329160794532188335953423432061490990243657757029868371504908982723472783555205531204141550984858016925351936

Methods

Step-by-step from math tutor: finding 64 to the power of 76

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:

647664^{76}

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

64 x 64 x 64 x 64 x ... (for a total of 76 times) = 186070713419675363980626894819329160794532188335953423432061490990243657757029868371504908982723472783555205531204141550984858016925351936

Therefore, 64 to the power of 76 is 186070713419675363980626894819329160794532188335953423432061490990243657757029868371504908982723472783555205531204141550984858016925351936.

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