Question

please answer it with explanation

tomorrow is my exam

Answer 1

b^(1/n)=a^(1/m)=c^(1/p)=k
b^(1/n)=k
then,b=k^n
a=k^m
c=k^p

now,
a×b×c=k^n ×k^m ×k^p
=k^(m+n+p)
then,1=k^(m+n+p) as,abc=1
then,k^0 = k^(m+n+p)
then,0=m+n+p

Answer 2

Let,

=> a^1/m=b^1/n=c^1/p = K (say)

Now,

=> a^1/m = K
=> a = K^m -------(1)

Similarly,

=> b = K^n --------(2)
=> c = K^p ---------(3)

Multiply all three equations :-

=> abc = K^m x K^n x K^p
Hence, base is equal, and abc=1

=> 1 = K^m+n+p
As we know that when any number that Power 0. then its value will be 1.
=> K^0 = K^m+n+p
Both K will cancel eachother,

=> 0 = m+n+p

or

=> m+n+p = 0



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