Math Tutor Explains: What is 75 to the Power of 78?

A math tutor would explain that to solve for 75 to the power of 78, we must first understand the structure. The number 75 is called the base, and the number 78 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 78 is equal to 179795386868031070255661663314108444526349461273020332273314146528677768306351865514065577860095693362601533549227639241507858969271183013916015625

Methods

Step-by-step from math tutor: finding 75 to the power of 78

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:

757875^{78}

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

75 x 75 x 75 x 75 x ... (for a total of 78 times) = 179795386868031070255661663314108444526349461273020332273314146528677768306351865514065577860095693362601533549227639241507858969271183013916015625

Therefore, 75 to the power of 78 is 179795386868031070255661663314108444526349461273020332273314146528677768306351865514065577860095693362601533549227639241507858969271183013916015625.

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