Math Tutor Explains: What is 68 to the Power of 66?

A math tutor would explain that to solve for 68 to the power of 66, we must first understand the structure. The number 68 is called the base, and the number 66 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: 68 to the Power of 66 is equal to 8822430353433127879427852383858908826126849786538535477220142654621892581432841851381170515894945169820082302669893402624

Methods

Step-by-step from math tutor: finding 68 to the power of 66

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:

686668^{66}

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

68 x 68 x 68 x 68 x ... (for a total of 66 times) = 8822430353433127879427852383858908826126849786538535477220142654621892581432841851381170515894945169820082302669893402624

Therefore, 68 to the power of 66 is 8822430353433127879427852383858908826126849786538535477220142654621892581432841851381170515894945169820082302669893402624.

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