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If a=x y^(p-1),\ b=x y^(q-1) and c=x y^(...

If `a=x y^(p-1),\ b=x y^(q-1)` and `c=x y^(r-1)` , prove that `a^(q-r)b^(r-p)c^(p-q)=1`

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RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
  1. If 1176=2^a xx\ 3^b xx\ 7^c , and a , b\ a n d\ c are natural numbers...

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  2. Given 4725=3^a5^b7^c , find the integral values of a ,\ b\ a n d\ c t...

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  3. If a=x y^(p-1),\ b=x y^(q-1) and c=x y^(r-1) , prove that a^(q-r)b^(r...

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  4. Find the value of: (8/(27))^(1/3)

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  5. Find the value of : ((32)/(243))^(1/5)

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  6. Find the value of: (1/(64))^(1/6)

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  7. Evaluate each of the following (i) (64)^(1/3) (ii)(125)^((-1)/3) (ii...

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  8. Evaluate each of the following by removing radical signs and negative ...

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  9. Simplify each of the following: (i)\ (625)^(-1/4) (ii)\ ((256)/(81))^(...

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  10. Simplify each of the following: (i)\ ((243)/(32))^(-4/5) (ii)\ (32...

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  11. [{(625)^(-1/4)}^(-1/2)]^2

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  12. Simplify: (256)^-(4^(((-3)/2)))

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  13. Simplify: 4/((216)^(-2/3))+1/((256)^(-3/4))+2/((243)^(-1/5))

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  14. Simplify: sqrt(1/4)+(0. 01)^(-1/2)-(27)^(2/3)

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  15. Simplify ((25)^(3/2)xx(243)^(3/5))/((16)^(5/4)xx(8)^(4/3)) (16xx 2^(n...

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  16. Simplify: ((81)/(16))^(-3/4)xx[((25)/9)^((-3)/2)-:(5/2)^(-3)]

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  17. Simplify each of the following by removing radical signs and negative ...

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  18. Simplify each of the following by removing radical signs and negative ...

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  19. Assuming that x , y , z are positive real numbers, simplify each of th...

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  20. Assuming that x , y , z are positive real numbers, simplify each of th...

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