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Show That: `[{X^(A(A-b))/X^(A(A+B))}Div{X^(B(B-a))/X^(B(B+A))}]^(A+B)=1` - CBSE Class 9 - Mathematics

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Question

Show that:

`[{x^(a(a-b))/x^(a(a+b))}div{x^(b(b-a))/x^(b(b+a))}]^(a+b)=1`

Solution

`[{x^(a(a-b))/x^(a(a+b))}div{x^(b(b-a))/x^(b(b+a))}]^(a+b)=1`

LHS = `[{x^(a(a-b))/x^(a(a+b))}div{x^(b(b-a))/x^(b(b+a))}]^(a+b)`

`=[{x^(a(a-b))/x^(a(a+b))}xx{x^(b(b+a))/x^(b(b-a))}]^(a+b)`

`=[{x^(a^2-ab)/x^(a^2+ab)}xx{x^(b^2+ab)/x^(b^2-ab)}]^(a+b)`

`=[{x^(a^2-ab-a^2-ab)}xx{x^(b^2+ab-b^2+ab)}]^(a+b)`

`=[x^(-2ab)xx x^(2ab)]^(a+b)`

`=[x^(-2ab+2ab)]^(a+b)`

`=[x^0]^(a+b)`

= 1

= RHS

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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: 4.2 | Page no. 25

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Solution Show That: `[{X^(A(A-b))/X^(A(A+B))}Div{X^(B(B-a))/X^(B(B+A))}]^(A+B)=1` Concept: Laws of Exponents for Real Numbers.
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