Math Tutor Explains: What is 81 to the Power of 86?

A math tutor would explain that to solve for 81 to the power of 86, we must first understand the structure. The number 81 is called the base, and the number 86 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 86 is equal to 134806745333774999112544281108398762007604655842244477571882977030779380134578775342851931269350457135570573724739071148715794846730641753406450349374737686315878881

Methods

Step-by-step from math tutor: finding 81 to the power of 86

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:

818681^{86}

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

81 x 81 x 81 x 81 x ... (for a total of 86 times) = 134806745333774999112544281108398762007604655842244477571882977030779380134578775342851931269350457135570573724739071148715794846730641753406450349374737686315878881

Therefore, 81 to the power of 86 is 134806745333774999112544281108398762007604655842244477571882977030779380134578775342851931269350457135570573724739071148715794846730641753406450349374737686315878881.

Math Tutor Suggests: Try related exponent problems

Our math tutors suggest reviewing other exponent problems that you can practice with!

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