# Digital Electronics - Digital Concepts - Discussion

Discussion Forum : Digital Concepts - General Questions (Q.No. 1)

1.

Any number with an exponent of zero is equal to:

Discussion:

47 comments Page 1 of 5.
Amani said:
2 years ago

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

Syed Shakeeb said:
2 years ago

Exponent refers to the number of times a number is multiplied by itself.

For example,

2/2=1.

For example,

2/2=1.

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Chandrakant said:
8 years ago

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

Abadi said:
8 years ago

What if the base number is zero?

Sharmi said:
8 years ago

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

Raju said:
8 years ago

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

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V.swetha reddy said:
8 years ago

As per mathematics anything power 0 is eual to 1.

S.Daisy Deva Priya said:
8 years ago

Any number with a power zero is equal to 1.

Hassan ali shah said:
8 years ago

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.

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

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

Malik aamir said:
8 years ago

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.

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.

(1)

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