Math Tutor Explains: What is 71 to the Power of 95?

A math tutor would explain that to solve for 71 to the power of 95, we must first understand the structure. The number 71 is called the base, and the number 95 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: 71 to the Power of 95 is equal to 74053080340222161236371298227184080672899632813693471670682855138706213582252972727799162669484794582145494906778171691317513825750026308076030545083543192707734235855511980151

Methods

Step-by-step from math tutor: finding 71 to the power of 95

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:

719571^{95}

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

71 x 71 x 71 x 71 x ... (for a total of 95 times) = 74053080340222161236371298227184080672899632813693471670682855138706213582252972727799162669484794582145494906778171691317513825750026308076030545083543192707734235855511980151

Therefore, 71 to the power of 95 is 74053080340222161236371298227184080672899632813693471670682855138706213582252972727799162669484794582145494906778171691317513825750026308076030545083543192707734235855511980151.

Math Tutor Suggests: Try related exponent problems

Our math tutors suggest reviewing other exponent problems that you can practice with!

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