Digital Electronics - Digital Concepts - Discussion

We know that mathematically something to the power zeo = 1.

e.g - x^0=1.

As we know that any thing power zero is always zero.

a^0=1.

We know that anything to the power of zero is equal to 1.

Any number to power zero is always 0 scientifically.

As per mathematical rule any number^0 is 1.

(number)^0 = 1.

According to me any a^(0) can be written as a^(k-k) , k being any non zero scalar, and so we have a^(k-k) = (a^k)/(a^k) = 1. So the answer is definitely 1.

Zero power of any number is value is 1.

It's one thing for me to tell you that any number raised to the zero power is equal to one, but what if you didn't believe me? Well, here's the proof.

We need to start by looking at the rule for multiplying exponents.

n^3*n^4 = (n*n*n)*(n*n*n*n) = n^7.

n^6*n^2 = (n*n*n*n*n*n)*(n*n) = n^8.

Did you notice a shortcut in that? As long as the bases are the same, to multiply any two terms with exponents, just add the exponents. Since math is a logical study, most rules work the same in all cases. So, let's try with a zero exponent.

x^4* x^0 = x^(4+0) = x^4.

As you can see, nothing changed. So we need to ask ourselves the question, what is the only number that when you multiply something by it, nothing changes?

The only answer to that question is 1. When you multiply something by 1, it does not change. So the only thing to conclude with our example above is that x^0 = 1.

x^4*x^0 = x^4.

x^4 * 1 = x^4.

Therefore, x^0 = 1.

This pattern plays out no matter what numbers or variables we use, so we can say that any term (except zero) raised to the zero power is equal to one.

As x^y/x^y = 1.

This implies by exponent rules x^y.x^(-y) = 1.

or x^(y-y) = 1 or x^0 = 1.

Any number with a power zero is equal to 1.