Math Tutor Explains: What is 49 to the Power of 63?

A math tutor would explain that to solve for 49 to the power of 63, we must first understand the structure. The number 49 is called the base, and the number 63 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: 49 to the Power of 63 is equal to 30363584636685952977761483300842317761884830962342835712214251124211986029046959176627705345482312365245649

Methods

Step-by-step from math tutor: finding 49 to the power of 63

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:

496349^{63}

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

49 x 49 x 49 x 49 x ... (for a total of 63 times) = 30363584636685952977761483300842317761884830962342835712214251124211986029046959176627705345482312365245649

Therefore, 49 to the power of 63 is 30363584636685952977761483300842317761884830962342835712214251124211986029046959176627705345482312365245649.

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