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# If A=X^(M+N)Y^L, B=X^(N+L)Y^M and C=X^(L+M)Y^N, Prove that A^(M-n)B^(N-l)C^(L-m)=1 - CBSE Class 9 - Mathematics

ConceptLaws of Exponents for Real Numbers

#### Question

If a=x^(m+n)y^l, b=x^(n+l)y^m and c=x^(l+m)y^n, Prove that a^(m-n)b^(n-l)c^(l-m)=1

#### Solution

Given a=x^(m+n)y^l, b=x^(n+l)y^m and c=x^(l+m)y^n

Putting the values of a, b and c in a^(m-n)b^(n-l)c^(l-m), we get

a^(m-n)b^(n-l)c^(l-m)

=(x^(m+n)y^l)^(m-n)(x^(n+l)y^m)^(n-l)(x^(l+m)y^n)^(l-m)

=[x^((m+n)(m-n))y(l(m-n))][x^((n+l)(n-l))y^(m(n-l))][x^((l+m)(l_m))y^(n(l-m))]

=x^((m^2-n^2))x^((n^2-l^2))x^((l^2-m^2))y^(lm-ln)y^(mn-ml)y^(nl-nm)

=x^0y^0

= 1

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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: 23.1 | Page no. 27

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Solution If A=X^(M+N)Y^L, B=X^(N+L)Y^M and C=X^(L+M)Y^N, Prove that A^(M-n)B^(N-l)C^(L-m)=1 Concept: Laws of Exponents for Real Numbers.
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