Math Tutor Explains: What is 65 to the Power of 67?

A math tutor would explain that to solve for 65 to the power of 67, we must first understand the structure. The number 65 is called the base, and the number 67 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: 65 to the Power of 67 is equal to 29187365396114890597188400984128508697423350109996193937071520582909195620468210431719402464523227536119520664215087890625

Methods

Step-by-step from math tutor: finding 65 to the power of 67

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:

656765^{67}

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

65 x 65 x 65 x 65 x ... (for a total of 67 times) = 29187365396114890597188400984128508697423350109996193937071520582909195620468210431719402464523227536119520664215087890625

Therefore, 65 to the power of 67 is 29187365396114890597188400984128508697423350109996193937071520582909195620468210431719402464523227536119520664215087890625.

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