Math Tutor Explains: What is 81 to the Power of 70?

A math tutor would explain that to solve for 81 to the power of 70, we must first understand the structure. The number 81 is called the base, and the number 70 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: 81 to the Power of 70 is equal to 39260092771818149473052557510879008881531271834245376524351437833098473006934585226108508724996140473513172757995825977888878576741601

Methods

Step-by-step from math tutor: finding 81 to the power of 70

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:

817081^{70}

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

81 x 81 x 81 x 81 x ... (for a total of 70 times) = 39260092771818149473052557510879008881531271834245376524351437833098473006934585226108508724996140473513172757995825977888878576741601

Therefore, 81 to the power of 70 is 39260092771818149473052557510879008881531271834245376524351437833098473006934585226108508724996140473513172757995825977888878576741601.

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