Math Tutor Explains: What is 66 to the Power of 52?

A math tutor would explain that to solve for 66 to the power of 52, we must first understand the structure. The number 66 is called the base, and the number 52 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: 66 to the Power of 52 is equal to 41331831306918030644048626551293171200056712794190786938755085532795628914236647031301635833856

Methods

Step-by-step from math tutor: finding 66 to the power of 52

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:

665266^{52}

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

66 x 66 x 66 x 66 x ... (for a total of 52 times) = 41331831306918030644048626551293171200056712794190786938755085532795628914236647031301635833856

Therefore, 66 to the power of 52 is 41331831306918030644048626551293171200056712794190786938755085532795628914236647031301635833856.

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