If a, m, n are positive integers, then \(\{m\sqrt{n\sqrt{a}}\}^{mn}\)

1.	If a, m, n are positive integers, then \(\{m\sqrt{n\sqrt{a}}\}^{mn}\) is equal toA. amnB. aC. am/nD. 1
Answer» \(\{m\sqrt{n\sqrt{a}}\}^{mn}\) We know for any non-zero number a, a^m × aⁿ = a^m+n = ^{\(\{(a^{\frac{1}{n}})^{\frac{1}{m}}\}^{mn}\)} Again using (a^m)ⁿ = a^mn we get, = \(\{a^{\frac{1}{mn}}\}^{mn}\) = a

If a, m, n are positive integers, then \(\{m\sqrt{n\sqrt{a}}\}^{mn}\) is equal toA. amnB. aC. am/nD. 1

Answer»

\(\{m\sqrt{n\sqrt{a}}\}^{mn}\)

We know for any non-zero number a,

a^m × aⁿ = a^m+n

= ^{\(\{(a^{\frac{1}{n}})^{\frac{1}{m}}\}^{mn}\)}

Again using (a^m)ⁿ = a^mn we get, = \(\{a^{\frac{1}{mn}}\}^{mn}\) = a