Question

Prove that;

$1) \: {x}^{0} = 1$
$2)also \: prove \: why \: not \: {0}^{0} = 1$
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Answer 1

Hey !!!

Solution :-

x^ 0 = 1 How ?

it's too simple to proove .

Let us see how .

x^ 0 = x^ 1 - 1 ( we can say ) yes we can say or write

since, x^ 1 - 1 = x ¹ * x-¹

We know x¹ = 1 and x-¹ = 1/x

since, x¹ × x -¹ = x × 1/x = 1

since x^ 0 = 1 prooved ♻

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Answer : Q :- 2

Using same process here
=> 0 ^ 0 = 0 ^ 1 - 1

=> 0^ 1 × 0 ^ - 1

=> 0 × 1/0 ( a/q to bodmas )



∴ 1/0 = ∞ since

0^ 0 = not defined or ∞

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Hope it helps you !!!

@Mr.Rajukumar111

Answer 2

Hi dude.....

TO PROVE:X POWER 0=1

Proof:
X^0 can be written as x^1-1
x^1-1=1
x^0=1

HENCE PROVED.

It is commonly taught that any number to the zero power is 1, and zero to any power is 0. But if that is the case, what is zero to the zero power? Well, it is undefined (since xy as a function of 2 variables is not continuous at the origin).


HOPE THIS HELPS U....♥♥