Math Tutor Explains: What is 75 to the Power of 81?

A math tutor would explain that to solve for 75 to the power of 81, we must first understand the structure. The number 75 is called the base, and the number 81 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: 75 to the Power of 81 is equal to 75851178834950607764107264210639500034553678974555452677804405566785933504242193263746415659727870637347521966080410305011128002661280333995819091796875

Methods

Step-by-step from math tutor: finding 75 to the power of 81

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:

758175^{81}

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

75 x 75 x 75 x 75 x ... (for a total of 81 times) = 75851178834950607764107264210639500034553678974555452677804405566785933504242193263746415659727870637347521966080410305011128002661280333995819091796875

Therefore, 75 to the power of 81 is 75851178834950607764107264210639500034553678974555452677804405566785933504242193263746415659727870637347521966080410305011128002661280333995819091796875.

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