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For every natural number k, which of the following is true?

For every natural number k, which of the following is true? Correct Answer (mn)k = mknk

In the first step, for k = 1, (mn)1 = m1n1 = mn, hence it is true. Let us assume the statement is true for k = l, Now by induction assumption, (mn)1 = m1n1 is true. So, to prove, (mn)l+1 = ml + 1nl+1, we have (mn)l = mlnl and multiplying both sides by (mn) ⇒ (mn)1(mn)=(m1n1)(mn) ⇒ (mn)l+1 = (mm1)(nn1) ⇒ (mn)l+1 = (ml+1nl+1). Hence, it is proved. So, (mn)k = mknk is true for every natural number k.

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