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If x , y ,z are positive real numbers sh...

If `x , y ,z` are positive real numbers show that: `sqrt(x^(-1)y)dotsqrt(y^(-1)z)dotsqrt(z^(-1)x)=1`

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To show that \[ \sqrt{x^{-1}y} \cdot \sqrt{y^{-1}z} \cdot \sqrt{z^{-1}x} = 1, \] we will simplify the left-hand side step by step. ...
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RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
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  2. Simplify: ((81)/(16))^(-3/4)xx[((25)/9)^(-3/2)-:(5/2)^(-3)]

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  3. If x , y ,z are positive real numbers show that: sqrt(x^(-1)y)dotsqrt(...

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  5. Evaluate each of the following (i)((11)/(12))^3 (ii) (3/4)^(-3)

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  6. Evaluate each of the following: (i) (2/(11))^4 xx ((11)/3)^2 xx (3/2)...

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  7. Evaluate each of the following: (i)\ 2^(55)xx\ 2^(60)-\ 2^(97)xx\ 2^(...

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  8. If a=2 and b=3 , then find the values of each of the following: a^a+b^...

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  9. If a=2 and b=3 , then find the values of each of the following: (a/b)^...

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  10. Simplify the following (ii)(3a^4b^3)(18 a^3b^5) (ii) (3a^7b^6)/(18 ...

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  11. Simplify each of the following: (a)\ (7^n-3\ xx\ 7^(n+1))/(20\ xx\ 7^n...

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  12. If (9^n\ xx\ 3^2\ xx\ (3^(-n/2))^(-2)-\ 27^n)/(3^(3m)\ xx\ 2^3)=1/(27)...

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  13. Assuming that x is a positive real number and a , b , c are rational n...

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  14. Assuming that x is a positive real number and a ,\ b ,\ c are rational...

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  15. Assuming that x is a positive real number and a ,\ b ,\ c are rational...

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  16. Assuming that x is a positive real number and a ,b , c are rational nu...

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  17. If x is a positive real number and the exponents are rational number...

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  18. Show that: (i) (x^(a(b-c)))/(x^(b(a-c)))-:((x^b)/(x^a))^c=1, (ii) (...

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  19. Show that: 1/(1+x^(b-a)+x^(c-a))+1/(1+x^(a-b)+\ x^(c-b))+1/(1+x^(b-c)+...

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  20. If a b c=1, show that 1/(1+a+b^(-1))+1/(1+b+c^(-1))+1/(1+c+a^(-1))=1

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