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Show that : ( A^M/A^-n)^( M - N ) Xx (A^N/A^-l)^( N - L) Xx (A^L/A^-m)^( L - M ) = 1 - Mathematics

Sum

Show that :
`( a^m/a^-n)^( m - n ) xx (a^n/a^-l)^( n - l) xx (a^l/a^-m)^( l - m ) = 1`

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Solution

`( a^m/a^-n)^( m - n ) xx (a^n/a^-l)^( n - l) xx (a^l/a^-m)^( l - m ) = 1`

= `( a^m xx a^n )^( m - n ) xx ( a^n xx a^l )^( n - l ) xx ( a^l xx a^m )^( l - m )`

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

= `a^( m^2 - n^2 ) xx a^( n^2 - l^2 ) xx a^( l^2 - m^2 )`

= `a^( m^2 - n^2 + n^2 - l^2 + l^2 - m^2 )`

= `a^0`
= 1

Concept: Laws of Exponents
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (A) | Q 8 | Page 98
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