If x = a m + n , y = a n + l and z = a l + m , prove that x m y n z l = x n y l z m .

Substituting values of x, y and z in L.H.S. of x m y n z l = x n y l z m we get, x m y n z l = (a m + n ) m .(a n + l ) n .(a l + m ) l = a m 2 + mn .a n 2 + ln .a lm + l 2 = a m 2 + n 2 + l 2 + mn + lm + ln .......(i) Substituting values of x, y and z in R.H.S. of x m y n z l = x n y l z m we get, x n y l z m = (a m + n ) n .(a n + l ) l .(a l + m ) m = a mn + n 2 .a nl + l 2 .a lm + m 2 = a m 2 + n 2 + l 2 + mn + lm + ln .........(ii) Since (i) = (ii), Hence, proved that x m y n z l = x n y l z m .

Mathematics

If x = a^{m + n}, y = a^{n + l} and z = a^{l + m}, prove that x^myⁿz^l = xⁿy^lz^m.

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Substituting values of x, y and z in L.H.S. of x^myⁿz^l = xⁿy^lz^m we get,

x^myⁿz^l = (a^{m + n})^m.(a^{n + l})ⁿ.(a^{l + m})^l

= a^{m² + mn}.a^{n² + ln}.a^{lm + l²}

= a^{m² + n² + l² + mn + lm + ln} …….(i)

Substituting values of x, y and z in R.H.S. of x^myⁿz^l = xⁿy^lz^m we get,

xⁿy^lz^m = (a^{m + n})ⁿ.(a^{n + l})^l.(a^{l + m})^m

= a^{mn + n²}.a^{nl + l²}.a^{lm + m²}

= a^{m² + n² + l² + mn + lm + ln} ………(ii)

Since (i) = (ii),

Hence, proved that x^myⁿz^l = xⁿy^lz^m.

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Mathematics

If x = a^{m + n}, y = a^{n + l} and z = a^{l + m}, prove that x^myⁿz^l = xⁿy^lz^m.

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Answer

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