Question

Here's an interesting questions !
What's 0⁰ ?

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Answer 1

Sorry the previous was a wrong one.

Here's the correct answer !!

In this question, we have to find 0 raise to the power 0.

Actually it's an indeterminate quantity. But according to Combinatorics (Branch of mathematics which deals with counting) , it's value is 1 which is contradicted to the one by Mathematical analysis (limits) where sometimes this expression is left undefined.

Let's firstly understand about the behaviour of 0 as a base.

⇒ 0¹ = 0

⇒ 0² = 0

⇒ 0³ = 0

⇒ 0⁴ = 0

⇒ 0⁵ = 0

On the other hand it's behaviour as exponent is different.

⇒ 1⁰ = 1

⇒ 2⁰ = 1

⇒ 3⁰ = 1

⇒ 4⁰ = 1

⇒ 5⁰ = 1

But if we talk about 0⁰, the contradiction arises whether it's value would be 0 or 1 as both exponent as well as base is 0 and no two values can be assigned to an expression. Because of this contradiction it's value is left indeterminate.

Answer 2

1

Step-by-step explanation:

0⁰ is 1.

Usually, we think that 0 have any exponent = 0.

like :-

0¹ = 0

0² = 0

0⁷ = 0

0ⁿ = 0....[where n is a natural number]

But If any number has exponent as 0, it is equal to 1.

like :-

1⁰ = 1

2⁰ = 1

3⁰ = 1

As same as when 0 have exponent as 1, it will be equal to 1.

Note :-

When 0 have any power (except 1) = 0

And any number's power 0 = 1

Hope it helps.