Question

If (a^m)^n = a^m.a^n , find the value of : m(n-1) - (n-1)
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Answer 1

Step-by-step explanation:

mn=m+n

m[n-1]=n

acc to question

=n-n+1

=1

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

We are aware of the identity of indices that

1.

$( { {a}^{m}) }^{n} = {a}^{mn}$

2.

${a}^{m} \times {a}^{n} = {a}^{m + n}$

GIVEN

$( { {a}^{m}) }^{n} = {a}^{m} \times {a}^{n}$

TO DETERMINE

$m(n - 1) - (n - 1)$

EVALUATION

$( { {a}^{m}) }^{n} = {a}^{m} \times {a}^{n}$

$\implies \: {a}^{mn}= {a}^{m + n}$

Comparing both sides we get

$\implies \: mn \: = m + n$

So

$m(n - 1) - (n - 1)$

$= mn - m - n + 1$

$= m + n - m - n + 1$

$= 1$