Math Tutor Explains: What is 66 to the Power of 90?

A math tutor would explain that to solve for 66 to the power of 90, we must first understand the structure. The number 66 is called the base, and the number 90 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: 66 to the Power of 90 is equal to 57405591836954697286570601016603564839189708308424902221163236220951005057911502176484785420010184797238188858040027239004486879201353285830167732422830590814846976

Methods

Step-by-step from math tutor: finding 66 to the power of 90

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:

669066^{90}

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

66 x 66 x 66 x 66 x ... (for a total of 90 times) = 57405591836954697286570601016603564839189708308424902221163236220951005057911502176484785420010184797238188858040027239004486879201353285830167732422830590814846976

Therefore, 66 to the power of 90 is 57405591836954697286570601016603564839189708308424902221163236220951005057911502176484785420010184797238188858040027239004486879201353285830167732422830590814846976.

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