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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

ConceptLaws of Exponents for Real Numbers

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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