Math Tutor Explains: What is 75 to the Power of 70?

A math tutor would explain that to solve for 75 to the power of 70, we must first understand the structure. The number 75 is called the base, and the number 70 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 70 is equal to 179592599813797960985749775445106096943740867154224363601035145662298829808338299928818803698205019969691420556046068668365478515625

Methods

Step-by-step from math tutor: finding 75 to the power of 70

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:

757075^{70}

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

75 x 75 x 75 x 75 x ... (for a total of 70 times) = 179592599813797960985749775445106096943740867154224363601035145662298829808338299928818803698205019969691420556046068668365478515625

Therefore, 75 to the power of 70 is 179592599813797960985749775445106096943740867154224363601035145662298829808338299928818803698205019969691420556046068668365478515625.

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