What is 23 to the Power of 77?

In order to solve for 23 to the power of 77, we must first understand the structure. The number 23 is called the base, and the number 77 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.

Solution: 23 to the Power of 77 is equal to 712924226912513004455728271323300657714052267955679067752437781532358642818400189341261477721474421502903

Methods

Step-by-step: finding 23 to the power of 77

The first step 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:

237723^{77}

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

23 x 23 x 23 x 23 x ... (for a total of 77 times) = 712924226912513004455728271323300657714052267955679067752437781532358642818400189341261477721474421502903

Therefore, 23 to the power of 77 is 712924226912513004455728271323300657714052267955679067752437781532358642818400189341261477721474421502903.

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