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Simplify: `Root(Lm)(X^L/X^M)Xxroot(Mn)(X^M/X^N)Xxroot(Nl)(X^N/X^L)` - CBSE Class 9 - Mathematics

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Question

Simplify:

`root(lm)(x^l/x^m)xxroot(mn)(x^m/x^n)xxroot(nl)(x^n/x^l)`

Solution

`root(lm)(x^l/x^m)xxroot(mn)(x^m/x^n)xxroot(nl)(x^n/x^l)`

`=(x^l/x^m)^(1/(lm))xx(x^m/x^n)^(1/(mn))xx(x^n/x^l)^(1/(nl))`

`=(x^(l-m))^(1/ml)xx(x^(m-n))^(1/mn)xx(x^(n-l))^(1/)nl`

`=x^((l-m)/(ml))xx x^((m-n)/(mn))xx x^((n-l)/(nl))`

`=x^((l-m)/(ml)+(m-n)/(mn)+(n-l)/(nl))`

`=x^((ln-mn+lm-nl+nm-lm)/(nml))`

`=x^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: 21.2 | Page no. 27

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Solution Simplify: `Root(Lm)(X^L/X^M)Xxroot(Mn)(X^M/X^N)Xxroot(Nl)(X^N/X^L)` Concept: Laws of Exponents for Real Numbers.
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