Math Tutor Explains: What is 65 to the Power of 86?

A math tutor would explain that to solve for 65 to the power of 86, we must first understand the structure. The number 65 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: 65 to the Power of 86 is equal to 813858064559603282051844244238151127874611550185793532362014585003930869964165221093818768880271153267736995232648801457120413260781788267195224761962890625

Methods

Step-by-step from math tutor: finding 65 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:

658665^{86}

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

65 x 65 x 65 x 65 x ... (for a total of 86 times) = 813858064559603282051844244238151127874611550185793532362014585003930869964165221093818768880271153267736995232648801457120413260781788267195224761962890625

Therefore, 65 to the power of 86 is 813858064559603282051844244238151127874611550185793532362014585003930869964165221093818768880271153267736995232648801457120413260781788267195224761962890625.

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