Math Tutor Explains: What is 76 to the Power of 86?

A math tutor would explain that to solve for 76 to the power of 86, we must first understand the structure. The number 76 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: 76 to the Power of 86 is equal to 562301103949521379698613444840483175786782674818543589621642673812795394802296799406081566993612667995758698956154199761193957206587307251266297903253705589784576

Methods

Step-by-step from math tutor: finding 76 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:

768676^{86}

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

76 x 76 x 76 x 76 x ... (for a total of 86 times) = 562301103949521379698613444840483175786782674818543589621642673812795394802296799406081566993612667995758698956154199761193957206587307251266297903253705589784576

Therefore, 76 to the power of 86 is 562301103949521379698613444840483175786782674818543589621642673812795394802296799406081566993612667995758698956154199761193957206587307251266297903253705589784576.

Math Tutor Suggests: Try related exponent problems

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