Question

New Question!

Prove: any number raised to power 0 = 1
Also, Explain your answer.
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Answer 1

Answer:

$\huge{\bf{\underline{\red{Answer :}}}}$

ᴛʜᴀᴛ ʀᴜʟᴇ ɪꜱ ɴᴏᴛ ᴠᴀʟɪᴅ ꜰᴏʀ ᴀʟʟ ᴛʜᴇ ɴᴜᴍʙᴇʀꜱ! ɪᴛ ɪꜱ ᴏɴʟʏ ᴠᴀʟɪᴅ ꜰᴏʀ ɴᴜᴍʙᴇʀꜱ ᴛʜᴀᴛ ᴀʀᴇ ᴅɪꜰꜰᴇʀᴇɴᴛ ꜰʀᴏᴍ ᴢᴇʀᴏ, ꜱɪɴᴄᴇ 0⁰ ʀᴇꜱᴜʟᴛꜱ ɪɴ ɪɴᴅᴇᴛᴇʀᴍɪɴᴀᴄʏ (ᴛʜᴇ ʀᴇꜱᴜʟᴛ ᴄᴀɴɴᴏᴛ ʙᴇ ᴅᴇᴛᴇʀᴍɪɴᴇᴅ).

ɪ ᴡɪʟʟ ʀᴇᴍᴇᴍʙᴇʀ ʏᴏᴜ ᴛʜᴀᴛ ɪɴ ᴇᴠᴇʀʏ ꜰʀᴀᴄᴛɪᴏɴ, ᴡʜᴇɴ ᴛʜᴇ ɴᴜᴍᴇʀᴀᴛᴏʀ ɪꜱ ᴇqᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ, ᴛʜᴇ ʀᴇꜱᴜʟᴛ ᴇqᴜᴀʟꜱ 1 (ᴏɴᴇ). ꜱᴏ $\dfrac{{a}^{m}}{{a}^{m}}$ = 1

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ɪꜰ ᴡᴇ ʜᴀᴠᴇ, ꜰᴏʀ ɪɴꜱᴛᴀɴᴄᴇ $\frac{2⁵}{2⁵}$ɪᴛꜱ ʀᴇꜱᴜʟᴛ ᴡɪʟʟ ʙᴇ ᴏɴᴇ ɪꜰ ᴡᴇ ᴀᴘᴘʟʏ ᴛʜᴇ ꜰɪʀꜱᴛ ʀᴜʟᴇ, ꜱɪɴᴄᴇ ᴛʜᴇ ɴᴜᴍᴇʀᴀᴛᴏʀ ɪꜱ ᴇQᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ. ɪꜰ ᴡᴇ ʜᴀᴅ ᴄʜᴏꜱᴇɴ ᴛʜᴇ ꜱᴇᴄᴏɴᴅ ʀᴜʟᴇ, ᴛʜᴇ ʀᴇꜱᴜʟᴛ

ᴡᴏᴜʟᴅ ʜᴀᴠᴇ ʙᴇᴇɴ $\frac{2⁵}{2⁵}$ = ${2}^{5-5}$ = 2⁰ ɪᴛ ɪꜱ ᴏʙᴠɪᴏᴜꜱ ᴛʜᴀᴛ ɴᴏ ᴍᴀᴛᴛᴇʀ ᴡʜᴀᴛ ʀᴜʟᴇ ɪꜱ ᴜꜱᴇᴅ, ᴡᴇ ʜᴀᴠᴇ ᴛᴏ ʀᴇᴀᴄʜ ᴛʜᴇ ꜱᴀᴍᴇ ᴠᴀʟᴜᴇ ᴀɴᴅ ɪᴛ ᴍᴇᴀɴꜱ ᴛʜᴀᴛ 2⁰ = 1

$\Rightarrow$In conclusion, every power having a 0 exponent, and whose base is different from 0, results in one.

Answer 2

$Why \: is \: (- x) {}^{0} \: = \: 1 \:$

$How \: is \: that \: proved?$

➙ So, Let's Start

↬ As we know that every Question have some sequence like, 2, 3, 4, 5, _ Here we need to find the no. after the 5 which is 6.

↬Now, Your this question is also based on the sequence :-

$Now \: here \: we \: need \: to \: prove \: that \: ( x) {}^{0}\: = \: 1$

Let the x be 2.

$So, \: 2 {}^{1} \: = \: 2$

$2 {}^{2} = 2 \times 2 = 4$

$2 {}^{3} = 2 \times 2 \times 2 = 8$

$2 {}^{4} = 2 \times 2 \times 2 \times 2 = 16$

${2}^{5} = 2 \times 2 \times 2 \times 2 \times 32$

So, Let's Start our Sequence :-

Here it is 32, 16, 8, 4, 2, __

Now we need to Found the no. next to the 2.

How to Found ??

We need to Divide

32 by 2 = 16

16 by 2 = 8

4 by 2 = 2

In the Similar Way,

If We will Divide 2 by 2 We will get 1.

$Hence \: Proved \: 2 {}^{0} \: = 1$

This Rule is valid for all the numbers.