Math Tutor Explains: What is 91 to the Power of 48?

A math tutor would explain that to solve for 91 to the power of 48, we must first understand the structure. The number 91 is called the base, and the number 48 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: 91 to the Power of 48 is equal to 10814011607783463018999168149593671727359466158094411777120051274102288312693257721106773325121

Methods

Step-by-step from math tutor: finding 91 to the power of 48

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:

914891^{48}

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

91 x 91 x 91 x 91 x ... (for a total of 48 times) = 10814011607783463018999168149593671727359466158094411777120051274102288312693257721106773325121

Therefore, 91 to the power of 48 is 10814011607783463018999168149593671727359466158094411777120051274102288312693257721106773325121.

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