Question

If x be any integer different from zero and m, n be any integers, then (x^m)ⁿ is equal to ______.

Options

• x^{m + n}

• x^mn

• `x^(m/n)`

• x^{m – n}

Answer 1

If x be any integer different from zero and m, n be any integers, then (x^m)ⁿ is equal to x^mn.

Explanation:

Using law of exponents,

(a^m)ⁿ = (a)^{m × n}  ...[∵ a is non-zero integer]

Similarly, (x^m)ⁿ = (x)^{m × n} = (x)^mn