# Why is a number raised to the power zero always given to be equal to one?

**Solution:**

Any number raised to a power is a form to represent numbers through exponents.

An exponent is expressed in the form 'a raised to the power b' as 'a^{b}'.

Let's prove this in steps. Let us consider any number a raised to the power b in the exponent as a^{b}.

When the exponent a^{b} is divided by itself, we get the expression:

a^{b }÷ a^{b}

Since we know a number divided by itself always results in 1, therefore, a^{b }÷ a^{b }= 1.

Also, a^{b }÷ a^{b} = a^{b }/a^{b} = a^{b - b} (Using the quotient law of exponents)

or, a^{b-b} = a^{0}

Using the two results of a^{b }÷ a^{b}, we get:

or, a^{0} = 1

Therefore, any number 'a' raised to the power zero is always equal to one as it's numerical value is 1.

## Why is a number raised to the power zero always given to be equal to one?

**Summary:**

Any number 'a' raised to the power zero is always equal to one because its numerical value is 1.

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