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Mathematics

If (am)n = am.an, find the value of :

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

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Answer

Given,

⇒ (am)n = am.an

⇒ amn = am + n

⇒ mn = m + n

⇒ mn - m = n

⇒ m(n - 1) = n

⇒ m = nn−1\dfrac{n}{n - 1} …….(1)

Substituting value of m from equation (1) in m(n - 1) - (n - 1), we get :

⇒m(n−1)−(n−1)=nn−1×(n−1)−(n−1)=n−(n−1)=n−n+1=1.\Rightarrow m(n - 1) - (n - 1) = \dfrac{n}{n - 1} \times (n - 1) - (n - 1) \\[1em] = n - (n - 1) \\[1em] = n - n + 1 \\[1em] = 1.

Hence, m(n - 1) - (n - 1) = 1.

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