Why is a number raised to the power zero always given to be equal to one?
Any number raised to a power is a form to represent numbers through exponents.
Answer: Any number 'a' raised to the power zero is always equal to one because its numerical value is 1.
An exponent is expressed in the form 'a raised to the power b' as 'ab'.
Let's prove this in steps. Let us consider any number a raised to the power b in the exponent as ab.
When the exponent ab is divided by itself, we get the expression:
ab ÷ ab
Since we know a number divided by itself always results in 1, therefore, ab ÷ ab = 1.
Also, ab ÷ ab = ab /ab = ab-b (Using the quotient law of exponents)
or, ab-b = a0
Using the two results of ab ÷ ab, we get:
or, a0 = 1
Therefore, any number 'a' raised to the power zero is always equal to one as it's numerical value is 1.