Math Tutor Explains: What is 65 to the Power of 94?

A math tutor would explain that to solve for 65 to the power of 94, we must first understand the structure. The number 65 is called the base, and the number 94 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 94 is equal to 259331650701120989352389556535971529393796905245306657074532418139754811089853804674212966008607793176012736390430534981407298942591987955808008337044157087802886962890625

Methods

Step-by-step from math tutor: finding 65 to the power of 94

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:

659465^{94}

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

65 x 65 x 65 x 65 x ... (for a total of 94 times) = 259331650701120989352389556535971529393796905245306657074532418139754811089853804674212966008607793176012736390430534981407298942591987955808008337044157087802886962890625

Therefore, 65 to the power of 94 is 259331650701120989352389556535971529393796905245306657074532418139754811089853804674212966008607793176012736390430534981407298942591987955808008337044157087802886962890625.

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