Math Tutor Explains: What is 65 to the Power of 71?

A math tutor would explain that to solve for 65 to the power of 71, we must first understand the structure. The number 65 is called the base, and the number 71 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: 65 to the Power of 71 is equal to 521012714424023368966436200317308960566942689057250809397937312105293460072620348837711158618279938536943518556654453277587890625

Methods

Step-by-step from math tutor: finding 65 to the power of 71

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:

657165^{71}

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

65 x 65 x 65 x 65 x ... (for a total of 71 times) = 521012714424023368966436200317308960566942689057250809397937312105293460072620348837711158618279938536943518556654453277587890625

Therefore, 65 to the power of 71 is 521012714424023368966436200317308960566942689057250809397937312105293460072620348837711158618279938536943518556654453277587890625.

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