Digital Electronics - Digital Concepts - Discussion

According to zero exponent rule any number raised to the power of zero always = 1.

Exponent refers to the number of times a number is multiplied by itself.
For example,
2/2=1.

I am not getting this, Please explain me in shortcut.

What if the base number is zero?

Anything power 0 is always 1, except zero power 0 according to the mathematical rules.

Example: 1^0, 2^0, 3^0, ........, n^0 = 1.

As per mathematics anything power 0 is eual to 1.

Any number with a power zero is equal to 1.

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.

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.