What is 78 to the Power of 25?

In order to solve for 78 to the power of 25, we must first understand the structure. The number 78 is called the base, and the number 25 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: 78 to the Power of 25 is equal to 200615769179944123990033289551061546247879917568

Methods

Step-by-step: finding 78 to the power of 25

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:

782578^{25}

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

78 x 78 x 78 x 78 x ... (for a total of 25 times) = 200615769179944123990033289551061546247879917568

Therefore, 78 to the power of 25 is 200615769179944123990033289551061546247879917568.

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