Math Tutor Explains: What is 85 to the Power of 87?

A math tutor would explain that to solve for 85 to the power of 87, we must first understand the structure. The number 85 is called the base, and the number 87 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: 85 to the Power of 87 is equal to 723513330298079423847813053757386980630894402504192331619131632274437691305545334768738196637665512111222836797145144774825076434965342997429615934379398822784423828125

Methods

Step-by-step from math tutor: finding 85 to the power of 87

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:

858785^{87}

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

85 x 85 x 85 x 85 x ... (for a total of 87 times) = 723513330298079423847813053757386980630894402504192331619131632274437691305545334768738196637665512111222836797145144774825076434965342997429615934379398822784423828125

Therefore, 85 to the power of 87 is 723513330298079423847813053757386980630894402504192331619131632274437691305545334768738196637665512111222836797145144774825076434965342997429615934379398822784423828125.

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