Math Tutor Explains: What is 48 to the Power of 50?

A math tutor would explain that to solve for 48 to the power of 50, we must first understand the structure. The number 48 is called the base, and the number 50 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: 48 to the Power of 50 is equal to 1153617588319010271378133306175011326520419737189530113840977835459429144159137562624

Methods

Step-by-step from math tutor: finding 48 to the power of 50

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:

485048^{50}

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

48 x 48 x 48 x 48 x ... (for a total of 50 times) = 1153617588319010271378133306175011326520419737189530113840977835459429144159137562624

Therefore, 48 to the power of 50 is 1153617588319010271378133306175011326520419737189530113840977835459429144159137562624.

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