Math Tutor Explains: What is 67 to the Power of 40?

A math tutor would explain that to solve for 67 to the power of 40, we must first understand the structure. The number 67 is called the base, and the number 40 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 40 is equal to 11040585568500089406404363834296492635119570897676624567608785151541319201

Methods

Step-by-step from math tutor: finding 67 to the power of 40

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:

674067^{40}

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

67 x 67 x 67 x 67 x ... (for a total of 40 times) = 11040585568500089406404363834296492635119570897676624567608785151541319201

Therefore, 67 to the power of 40 is 11040585568500089406404363834296492635119570897676624567608785151541319201.

Math Tutor Suggests: Try related exponent problems

Our math tutors suggest reviewing other exponent problems that you can practice with!

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