Math Tutor Explains: What is 51 to the Power of 68?

A math tutor would explain that to solve for 51 to the power of 68, we must first understand the structure. The number 51 is called the base, and the number 68 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: 51 to the Power of 68 is equal to 130248273326200756362276676780397038820843956703563558740123888619511231926885304862720912802236453848083636176448401

Methods

Step-by-step from math tutor: finding 51 to the power of 68

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:

516851^{68}

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

51 x 51 x 51 x 51 x ... (for a total of 68 times) = 130248273326200756362276676780397038820843956703563558740123888619511231926885304862720912802236453848083636176448401

Therefore, 51 to the power of 68 is 130248273326200756362276676780397038820843956703563558740123888619511231926885304862720912802236453848083636176448401.

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