mn√(xm/xn) × nl√(xn/xl) × lm√(xl/xm) = ?

^mn√(x^m/xⁿ) × ^nl√(xⁿ/x^l) × ^lm√(x^l/x^m) = ?

A x^lmn

B x^1/lmn

C 1

Solution

Correct Answer: Option C

^mn√(x^m/xⁿ) × ^nl√(xⁿ/x^l) × ^lm√(x^l/x^m)
= (x^m-n)^1/mn × (x^n-l)^1/nl × (x^l-m)^1/lm
= x^m-n/mn × x^n-l/nl × x^l-m^/lm
= x^{m-n/mn + n-l/nl + l-m/lm}
= x^{{l(m-n) + m(n-l) + n(l-m)}/mnl}
= x^{(lm - nl + mn - lm + nl - mn)/}^mnl
= x^0/mnl= x⁰
= 1

Solution

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