Math Tutor Explains: What is 36 to the Power of 69?

A math tutor would explain that to solve for 36 to the power of 69, we must first understand the structure. The number 36 is called the base, and the number 69 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: 36 to the Power of 69 is equal to 242589809215613984990578009590212203208248910334634260613591036504250373122777355949226063885245052948054016

Methods

Step-by-step from math tutor: finding 36 to the power of 69

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:

366936^{69}

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

36 x 36 x 36 x 36 x ... (for a total of 69 times) = 242589809215613984990578009590212203208248910334634260613591036504250373122777355949226063885245052948054016

Therefore, 36 to the power of 69 is 242589809215613984990578009590212203208248910334634260613591036504250373122777355949226063885245052948054016.

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