Math Tutor Explains: What is 96 to the Power of 64?

A math tutor would explain that to solve for 96 to the power of 64, we must first understand the structure. The number 96 is called the base, and the number 64 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: 96 to the Power of 64 is equal to 7334304125596190624668832643061791071911921761558623296040973972480495126634460976537700765146565217101386328744001668808441856

Methods

Step-by-step from math tutor: finding 96 to the power of 64

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:

966496^{64}

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

96 x 96 x 96 x 96 x ... (for a total of 64 times) = 7334304125596190624668832643061791071911921761558623296040973972480495126634460976537700765146565217101386328744001668808441856

Therefore, 96 to the power of 64 is 7334304125596190624668832643061791071911921761558623296040973972480495126634460976537700765146565217101386328744001668808441856.

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