Math Tutor Explains: What is 81 to the Power of 73?

A math tutor would explain that to solve for 81 to the power of 73, we must first understand the structure. The number 81 is called the base, and the number 73 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 73 is equal to 20864422962747809174108524216139051359009860634863197145477852473459685593278322907148331985320673889384314043682059753515243519702133177041

Methods

Step-by-step from math tutor: finding 81 to the power of 73

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:

817381^{73}

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

81 x 81 x 81 x 81 x ... (for a total of 73 times) = 20864422962747809174108524216139051359009860634863197145477852473459685593278322907148331985320673889384314043682059753515243519702133177041

Therefore, 81 to the power of 73 is 20864422962747809174108524216139051359009860634863197145477852473459685593278322907148331985320673889384314043682059753515243519702133177041.

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