Math Tutor Explains: What is 99 to the Power of 66?

A math tutor would explain that to solve for 99 to the power of 66, we must first understand the structure. The number 99 is called the base, and the number 66 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: 99 to the Power of 66 is equal to 515137117423803644429980410789004558123659486689659784966832951094733292177381847964722134800160137646898658467293025470746261443401

Methods

Step-by-step from math tutor: finding 99 to the power of 66

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:

996699^{66}

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

99 x 99 x 99 x 99 x ... (for a total of 66 times) = 515137117423803644429980410789004558123659486689659784966832951094733292177381847964722134800160137646898658467293025470746261443401

Therefore, 99 to the power of 66 is 515137117423803644429980410789004558123659486689659784966832951094733292177381847964722134800160137646898658467293025470746261443401.

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