Math Tutor Explains: What is 33 to the Power of 95?

A math tutor would explain that to solve for 33 to the power of 95, we must first understand the structure. The number 33 is called the base, and the number 95 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: 33 to the Power of 95 is equal to 1814781270208929096388947210512343868064670699229385182484704503664227225485971133181223287111625472438150496126629752547091283213093002376204257

Methods

Step-by-step from math tutor: finding 33 to the power of 95

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:

339533^{95}

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

33 x 33 x 33 x 33 x ... (for a total of 95 times) = 1814781270208929096388947210512343868064670699229385182484704503664227225485971133181223287111625472438150496126629752547091283213093002376204257

Therefore, 33 to the power of 95 is 1814781270208929096388947210512343868064670699229385182484704503664227225485971133181223287111625472438150496126629752547091283213093002376204257.

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