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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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RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. Simplify : ((25)^(3/2)*(243)^(3/5))/((16)^(5/4)*(8)^(4/3))

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  2. Simplify: ((81)/(16))^(-3/4)*[((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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  4. Evaluate each of the following (i) 5^2 x 5^4 (ii) 5^8 divide 5^3 (i...

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  5. Evaluate each of the following (i) (2/11)^4 x (11/3)^2 x (3/2)^3 (ii...

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  6. If a=2 and b=3 then find the values of each of the following (i) a^a...

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  7. Evaluate each of the following removing radical sign and negative indi...

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  8. Evaluate each of the following (i) 5^2\xx\ 5^4 (ii) (3^2)^3

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

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

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

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

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

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  14. Simplify the following (i) (3a^4b^3)(18 a^3b^5) (ii) (3a^7b^6)/(1...

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

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

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

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

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

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

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