Math Tutor Explains: What is 21 to the Power of 52?

A math tutor would explain that to solve for 21 to the power of 52, we must first understand the structure. The number 21 is called the base, and the number 52 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: 21 to the Power of 52 is equal to 569381465857367090636427305760163241950353347303833610101782245331441

Methods

Step-by-step from math tutor: finding 21 to the power of 52

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:

215221^{52}

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

21 x 21 x 21 x 21 x ... (for a total of 52 times) = 569381465857367090636427305760163241950353347303833610101782245331441

Therefore, 21 to the power of 52 is 569381465857367090636427305760163241950353347303833610101782245331441.

Math Tutor Suggests: Try related exponent problems

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

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