Math Tutor Explains: What is 46 to the Power of 89?

A math tutor would explain that to solve for 46 to the power of 89, we must first understand the structure. The number 46 is called the base, and the number 89 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: 46 to the Power of 89 is equal to 9670457478596417634875968147335522259235175612203691881056316268778885197255813979675255701605462883485795701450732339062526080650899504517041094656

Methods

Step-by-step from math tutor: finding 46 to the power of 89

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:

468946^{89}

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

46 x 46 x 46 x 46 x ... (for a total of 89 times) = 9670457478596417634875968147335522259235175612203691881056316268778885197255813979675255701605462883485795701450732339062526080650899504517041094656

Therefore, 46 to the power of 89 is 9670457478596417634875968147335522259235175612203691881056316268778885197255813979675255701605462883485795701450732339062526080650899504517041094656.

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