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If `X = A^(M+N),` `Y=A^(N+L)` and `Z=A^(L+M),` Prove that `X^My^Nz^L=X^Ny^Lz^M` - CBSE Class 9 - Mathematics

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Question

If `x = a^(m+n),` `y=a^(n+l)` and `z=a^(l+m),` prove that `x^my^nz^l=x^ny^lz^m`

Solution

Given `x = a^(m+n),` `y=a^(n+l)` and `z=a^(l+m)`

Putting the values ofx, y and z in `x^my^nz^l,` we get

`x^my^nz^l`

`=(a^(m+n))^m(a^(n+l))^n(a^(l+m))^l`

`=(a^(m^2+nm))(a^(n^2+ln))(a^(l^2+lm))`

`=a^(m^2+n^2+l^2+nm+ln+lm)`

Putting the values of x, y and z in `x^ny^lz^m,` we get

`x^ny^lz^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^(mn+n^2+nl+l^2+lm+m^2)`

So, `x^my^nz^l=x^ny^lz^m`

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APPEARS IN

 RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 2: Exponents of Real Numbers
Ex. 2.20 | Q: 23.2 | Page no. 27

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Solution If `X = A^(M+N),` `Y=A^(N+L)` and `Z=A^(L+M),` Prove that `X^My^Nz^L=X^Ny^Lz^M` Concept: Laws of Exponents for Real Numbers.
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