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For any positive real number x , find th...

For any positive real number `x ,` find the value of `((x^a)/(x^b))^(a+b)\ xx\ ((x^b)/(x^c))^(b+c)\ xx\ ((x^c)/(x^a))^(c+a)`

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Prove that: ((x^a)/(x^b))^c\xx\ ((x^b)/(x^c))^a\ xx\ ((x^c)/(x^a))^b=1

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Prove that: ((x^a)/(x^(b)))^(a^(2+a b+b^2))\ xx\ ((x^b)/(x^(c)))^(b^(2+b c+c^2))\ xx\ ((x^c)/(x^(a)))^(c^(2+c a+a^2))=1

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Assuming that x is a positive real number and a ,\ b ,\ c are rational numbers, show that: ((x^a)/(x^b))^(a+b)\ ((x^b)/(x^c))^(b+c)((x^c)/(x^a))^(c+a)=1

If x is a positive real number and the exponents are rational numbers, show that: ((x^a)/(x^b))^(a+b-c)\ ((x^b)/(x^c))^(b+c-a)((x^c)/(x^a))^(c+a-b)=1

Assuming that x is a positive real number and a ,\ b ,\ c are rational numbers, show that: ((x^a)/(x^b))^(1/(a b))\ ((x^b)/(x^c))^(1/(b c))\ \ ((x^c)/(x^a))^(1/(a c))=1

If x is a positive real number and the exponents are rational numbers, Find: ((x^a)/(x^b))^(a^2+b^2-a b). ((x^b)/x^c)^(b^2+c^2-b c). ((x^c)/(x^(a)))^(c^2+a^2-c a)

(x^a/x^b)^(a+b).(x^b/x^c)^(b+c).(x^c/x^a)^(c+a)

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RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. State the product law of exponents.

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  2. State the power law of exponents

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  3. For any positive real number x , find the value of ((x^a)/(x^b))^(a+b)...

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  4. Write the value of {5"("8^(-1/2)"}"^(-1/4)}^2

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  5. For any positive real number x;write the value of {(x^a)^b}^(1/(ab)) {...

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  6. If (x-1)^3=8, what is the value of (x+1)^2\ ?

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  7. If 2^4\ xx\ 4^2=16^x , then find the value of x ?

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  8. If 3^(x-1)=9 and 4^(y+2)=64 , what is the value of x/y\ ?

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  9. Write the value of root(3)(7)\ xx\root(3)( 49)

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  10. Write (1/9)^(-1/2)\ xx\ (64)^(-1/3) as a rational number.

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  11. Write the value of root(3)(125)\ xx\ root(3)(27)

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  12. The value of {2-3(2-3)^3}^3 is (a)5 (b) 125 (c) 1/5 (d) -12...

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  13. Which one is the correct option (256)^(0. 16)xx(256)^(0. 09)=? a. 4...

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  14. If 10^(2y)=\ 25\ , then 10^(-y) equals (a)-1/5 (b) 1/(50) (c)...

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  15. The value of x-y^(x-y) when x=2 and y=-2 is (a)18 (b) -18\ (c...

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  16. The product of the square root of x with the cube root of x is (a) cub...

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  17. if 9^(x+2)=240+9^x , then x= (a)0. 5 (b) 0.2 (c) 0.4 (d) 0.1

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  18. The seventh root of x divided by the eighth root of x is (a)x (b) ...

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  19. The square root of 64 divided by the cube root of 64 is (a)64 (b...

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  20. Which of the following is (are) not equal to {(5/6)^(1/5)}^(-1/6)\ ? ...

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