Math Tutor Explains: What is 78 to the Power of 69?

A math tutor would explain that to solve for 78 to the power of 69, we must first understand the structure. The number 78 is called the base, and the number 69 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: 78 to the Power of 69 is equal to 35853172087537808434998851286879243190253339114364824483789702763946769013271558352556459957035753483389180370950661418515020382208

Methods

Step-by-step from math tutor: finding 78 to the power of 69

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:

786978^{69}

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

78 x 78 x 78 x 78 x ... (for a total of 69 times) = 35853172087537808434998851286879243190253339114364824483789702763946769013271558352556459957035753483389180370950661418515020382208

Therefore, 78 to the power of 69 is 35853172087537808434998851286879243190253339114364824483789702763946769013271558352556459957035753483389180370950661418515020382208.

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