ToProve:Anypowerof1is1weallareawareofthefactthat(am)n=(an)mLetusputm=0,then(a0)n=(something)01n=1Henceproved.To\quad Prove\quad :\quad Any\quad power\quad of\quad 1\quad is\quad 1\\ we\quad all\quad are\quad aware\quad of\quad the\quad fact\quad that\\ { ({ a }^{ m }) }^{ n }\quad =\quad { ({ a }^{ n }) }^{ m }\\ Let\quad us\quad put\quad m\quad =\quad 0,\quad then\quad \\ { ({ a }^{ 0 }) }^{ n }\quad =\quad ({ something) }^{ 0 }\\ { 1 }^{ n }\quad =\quad 1\\ Hence\quad proved.ToProve:Anypowerof1is1weallareawareofthefactthat(am)n=(an)mLetusputm=0,then(a0)n=(something)01n=1Henceproved. Proof of the assumption I have used in the proof. a0=ab−bab−b=abab=1{ a }^{ 0 }\quad =\quad { a }^{ b-b }\\ { a }^{ b-b }\quad =\quad \frac { { a }^{ b } }{ { a }^{ b } } \quad =\quad \boxed { 1 } a0=ab−bab−b=abab=1 Credit to @ArchitBoobna
Note by Rajdeep Dhingra 6 years, 5 months ago
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How will you prove that 1^n=1 without proving a^0=1
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a0=ab−bab−b=abab=1{ a }^{ 0 }\quad =\quad { a }^{ b-b }\\ { a }^{ b-b }\quad =\quad \frac { { a }^{ b } }{ { a }^{ b } } \quad =\quad \boxed { 1 } a0=ab−bab−b=abab=1
Your explanation for a^0 is correct,but you have to prove this in your note.
Rajdeep, this proof is created by me, so please mention it.
Of course, we're making the assumption that 000^{0}00 is 1, correct?
No we are not... we can consider a is not equal to 0... instead of "a" we could have used any constant
Alright, just making sure...
@Tytan Le Nguyen – @Archit Boobna Whats ur score in NTSE Delhi held on 18 Dec. Btw what is score highest in FSD?
No we are not Please tell in which step am i using it
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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
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[example link](https://brilliant.org)> This is a quote# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"\(...\)or\[...\]to ensure proper formatting.2 \times 32^{34}a_{i-1}\frac{2}{3}\sqrt{2}\sum_{i=1}^3\sin \theta\boxed{123}Comments
How will you prove that 1^n=1 without proving a^0=1
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a0=ab−bab−b=abab=1
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Your explanation for a^0 is correct,but you have to prove this in your note.
Rajdeep, this proof is created by me, so please mention it.
Of course, we're making the assumption that 00 is 1, correct?
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No we are not... we can consider a is not equal to 0... instead of "a" we could have used any constant
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Alright, just making sure...
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@Archit Boobna Whats ur score in NTSE Delhi held on 18 Dec. Btw what is score highest in FSD?
No we are not Please tell in which step am i using it