# 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.
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.

(1)

Raju said:
8 years ago

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

(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)

Anirudh Sodhani said:
9 years ago

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.

K.VAMSI KRISHNA said:
1 decade ago

a^0 = 1.

"Anything power zero is always zero".

So answer is: B.

"Anything power zero is always zero".

So answer is: B.

Nandhini venkatachalapathy said:
1 decade ago

As per math rule anything power 0 is 1.

For eg: e^0 = 1.

For eg: e^0 = 1.

K.ANJINEYULUNAIK said:
1 decade ago

Any numerical no power zero is equivalent = 1.

UMAMAHESH.S said:
1 decade ago

A power Zero is 1. But when A=0 then it not satisfied condition.

Ramya.K said:
1 decade ago

Number x.

Exponential number e^x.

When x = 0.

e^0 = 1.

Exponential number e^x.

When x = 0.

e^0 = 1.

Anunay singh said:
1 decade ago

Exponent means power not exponential(e).

Thus,

For any real number (a says) with zero exponent means a^0.

And any number with power zero is equal to 1.

a^0=1.

Thus,

For any real number (a says) with zero exponent means a^0.

And any number with power zero is equal to 1.

a^0=1.

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