Math Tutor Explains: What is 33 to the Power of 77?

A math tutor would explain that to solve for 33 to the power of 77, we must first understand the structure. The number 33 is called the base, and the number 77 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: 33 to the Power of 77 is equal to 842506714222034986377665537243970265098661950508148501967088295783728612174508896092022189907905149812071917470663073

Methods

Step-by-step from math tutor: finding 33 to the power of 77

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:

337733^{77}

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

33 x 33 x 33 x 33 x ... (for a total of 77 times) = 842506714222034986377665537243970265098661950508148501967088295783728612174508896092022189907905149812071917470663073

Therefore, 33 to the power of 77 is 842506714222034986377665537243970265098661950508148501967088295783728612174508896092022189907905149812071917470663073.

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