Math Tutor Explains: What is 75 to the Power of 97?

A math tutor would explain that to solve for 75 to the power of 97, we must first understand the structure. The number 75 is called the base, and the number 97 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: 75 to the Power of 97 is equal to 76022570320154164480091054377813911753867812881741083004748195852252676763610588616052907185031487216474277854786135395181806036872961373075489877049193410130101256072521209716796875

Methods

Step-by-step from math tutor: finding 75 to the power of 97

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:

759775^{97}

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

75 x 75 x 75 x 75 x ... (for a total of 97 times) = 76022570320154164480091054377813911753867812881741083004748195852252676763610588616052907185031487216474277854786135395181806036872961373075489877049193410130101256072521209716796875

Therefore, 75 to the power of 97 is 76022570320154164480091054377813911753867812881741083004748195852252676763610588616052907185031487216474277854786135395181806036872961373075489877049193410130101256072521209716796875.

Math Tutor Suggests: Try related exponent problems

Our math tutors suggest reviewing other exponent problems that you can practice with!

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