Math Tutor Explains: What is 56 to the Power of 62?

A math tutor would explain that to solve for 56 to the power of 62, we must first understand the structure. The number 56 is called the base, and the number 62 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: 56 to the Power of 62 is equal to 2441505316867030688319681652488699602245249987716728870165115919651764742711003837140223368135574624650919936

Methods

Step-by-step from math tutor: finding 56 to the power of 62

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:

566256^{62}

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

56 x 56 x 56 x 56 x ... (for a total of 62 times) = 2441505316867030688319681652488699602245249987716728870165115919651764742711003837140223368135574624650919936

Therefore, 56 to the power of 62 is 2441505316867030688319681652488699602245249987716728870165115919651764742711003837140223368135574624650919936.

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