Question

A^(1/m) = b^(1/n) = c^(1/p) and abc=1. What is 'm+n+p'?

Answer 1

||✪✪ QUESTION ✪✪||

if a^(1/m) = b^(1/n) = c^(1/p) and abc=1. What is 'm+n+p'?

|| ✰✰ ANSWER ✰✰ ||

Let us assume that , a^(1/m) = b^(1/n) = c^(1/p) = K ( where k is any constant Number).

So,

→ a^(1/m) = k

→ a = k^m ---------- Equation (1)

Similarly,

→ b^(1/n) = k

→ b = k^n ------------ Equation (2)

And ,

→ c^(1/p) = k

→ c = k^p ------------- Equation (3)

now, given that, abc = 1 ,

Putting values of all Equations here , we get,

→ k^m * k^n * k^p = 1

or,

→ k^(m+n+p) = 1

Now, we know that, a^0 = 1 , or value of any power zero is Equal to 1. ,

So, RHS , can be written as ,

→ k^(m+n+p) = k^0

Comparing now, we get,

→ (m + n + p) = 0 (Ans).

Answer 2

Step-by-step explanation:

$\huge\underline\purple{\sf Question :-}$ A^(1/m) = b^(1/n) = c^(1/p) and abc=1. What is 'm+n+p'?

__________________________________

$\huge\underline\pink{\tt Answer :-}$ a^(1/m)= b^(1/n)=c^(1/p)=K

$\large\implies{\sf }$a=k^(1/1/m)=k^m

Similarly b= k^n and c= k^p

Now, abc= 1 ( Given)

$\large\implies{\sf }$k^m x k^n x k^p= 1

$\large\implies{\sf }$k^(m+n+p) =1=k^0

Hence, m+n+p= 0