Math Tutor Explains: What is 67 to the Power of 75?

A math tutor would explain that to solve for 67 to the power of 75, we must first understand the structure. The number 67 is called the base, and the number 75 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: 67 to the Power of 75 is equal to 90283877444679237707387884059775409403007857541108814530064805693861792673741154927482827289536015811128159160541968151628491209395008443

Methods

Step-by-step from math tutor: finding 67 to the power of 75

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:

677567^{75}

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

67 x 67 x 67 x 67 x ... (for a total of 75 times) = 90283877444679237707387884059775409403007857541108814530064805693861792673741154927482827289536015811128159160541968151628491209395008443

Therefore, 67 to the power of 75 is 90283877444679237707387884059775409403007857541108814530064805693861792673741154927482827289536015811128159160541968151628491209395008443.

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