Prove that anything raised to power zero is equal to one?

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Answer

Yes, I shall try to give easy to understand explanation with example:Let us first understand any nonzero number raised to zero is 1.Lets us start with simple example 5^3 & step by step we will reduce power.5^3 = 5 raised to 3 or cube of 5 = 5 * 5 * 5 ... (3 times). Simple you know.5^2 = 5 * 5 ... (2 times) = 5*5*5 .. (3 times) /5 = 5^3 /55^1 = 5 ... (1 time) = 5*5 .. (2 times)/5 = 5^2/5. With same anology ..5^0 = 5 ... 0 times??? = 5^1/5 = 15^(-1) = 5^0/5 = 1/55^(-2)= 5^(-1)/5 = (1/5)/5 = 1/ (5*5) = 1/(5^2) similarly5^(-r)= 1/(5^r) ... where r>0
So intermediate step in bold 5^0=1. For any non zero number n, n^0 =1.
Hope it help u

Answer

Proof that anything raised to power zero is equal to one

When we talk about an exponent, we are referring to the number of times that a base number will be multiplied by itself. For example, 2³ means that 2 will be multiplied by itself three times, resulting in 8. However, what happens when we raise a number to the power of zero?

Understanding Exponents

To understand why anything raised to power zero is equal to one, we need to first understand the basic rules of exponents. When we have a number raised to a power, the exponent tells us how many times we need to multiply that number by itself. For example:

2³ = 2 x 2 x 2 = 8

2⁴ = 2 x 2 x 2 x 2 = 16

2⁵ = 2 x 2 x 2 x 2 x 2 = 32

Zero as an Exponent

So what happens when we raise a number to the power of zero? According to the rules of exponents, any number raised to the power of zero is equal to one. Let's look at some examples:

2⁰ = 1

10⁰ = 1

x⁰ = 1

As you can see, no matter what number we raise to the power of zero, the result is always one. This is because when we raise a number to the power of zero, we are essentially saying that we don't want to multiply that number by itself at all. Instead, we want to multiply it by zero, which results in a value of one.

Conclusion

Therefore, it can be concluded that anything raised to power zero is equal to one. This rule is important in many mathematical concepts, including calculus and algebra, and it is essential to understand when working with exponents and other mathematical operations.

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