\[To\quad Prove\quad :\quad Any\quad power\quad of\quad 1\quad is\quad 1\\ we\quad all\quad are\quad aware\quad of\quad the\quad fact\quad that\\ { ({ a }^{ m }) }^{ n }\quad =\quad { ({ a }^{ n }) }^{ m }\\ Let\quad us\quad put\quad m\quad =\quad 0,\quad then\quad \\ { ({ a }^{ 0 }) }^{ n }\quad =\quad ({ something) }^{ 0 }\\ { 1 }^{ n }\quad =\quad 1\\ Hence\quad proved.\] Proof of the assumption I have used in the proof. \[{ a }^{ 0 }\quad =\quad { a }^{ b-b }\\ { a }^{ b-b }\quad =\quad \frac { { a }^{ b } }{ { a }^{ b } } \quad =\quad \boxed { 1 } \] Credit to @ArchitBoobna

## Comments

Sort by:

TopNewestHow will you prove that 1^n=1 without proving a^0=1 – Vishal S · 2 years, 6 months ago

Log in to reply

– Rajdeep Dhingra · 2 years, 6 months ago

\[{ a }^{ 0 }\quad =\quad { a }^{ b-b }\\ { a }^{ b-b }\quad =\quad \frac { { a }^{ b } }{ { a }^{ b } } \quad =\quad \boxed { 1 } \]Log in to reply

– Vishal S · 2 years, 6 months ago

Your explanation for a^0 is correct,but you have to prove this in your note.Log in to reply

Rajdeep, this proof is created by me, so please mention it. – Archit Boobna · 2 years, 6 months ago

Log in to reply

Of course, we're making the assumption that \(0^{0}\) is 1, correct? – Tytan Le Nguyen · 2 years, 6 months ago

Log in to reply

– Rajdeep Dhingra · 2 years, 6 months ago

No we are not Please tell in which step am i using itLog in to reply

– Archit Boobna · 2 years, 6 months ago

No we are not... we can consider a is not equal to 0... instead of "a" we could have used any constantLog in to reply

– Tytan Le Nguyen · 2 years, 6 months ago

Alright, just making sure...Log in to reply

@Archit Boobna Whats ur score in NTSE Delhi held on 18 Dec. Btw what is score highest in FSD? – Kaustubh Miglani · 6 months, 2 weeks ago

Log in to reply