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

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

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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)

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

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

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

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))

Simplify: (i)\ ((x^(a+b))/(x^c))^(a-b)\ ((x^(b+c))/(x^a))^(b-c)\ ((x^(c+a))/(x^b))^(c-a) (ii)\ ((x^l)/(x^m))^(1/(lm))\ xx\ ((x^m)/(x^n))^(1/(mn))\ xx\ \ ((x^n)/(x^l))^(1/(ln))

Assuming that x is a positive real number and a ,\ b ,\ c are rational numbers, show that: ((x^a)/(x^b))^(a^2+a b+b^2)((x^b)/(x^c))^(b^2+b c+c^2)((x^c)/(x^a))^(c^2+c a+a^2)=1

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

RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. Prove that: ((x^a)/(x^b))^(a^(2+a b+b^(2)))xx\ ((x^b)/(x^c))^(b^(2+b c...

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

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

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  4. Prove that: 1/(1+x^(a-b))+1/(1+x^(b-a))=1

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  5. Prove that: 1/(1+x^(b-a)+\ x^(c-a))+1/(1+x^(a-b)+\ x^(c-b))+1/(1+x^(b-...

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  6. Prove that: (a+b+c)/(a^(-1)\ b^(-1)+b^(-1)\ c^(-1)+c^(-1)a^(-1))=a b c

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  7. Prove that: (a^(-1)+b^(-1))^(-1)=(a b)/(a+b)

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  8. 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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  9. Simplify the following: (i)\ (3^n\ xx\ 9^(n+1))/(3^(n-1)\ xx\ 9^(n-1))...

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  10. Simplify the following: (i)\ (5^(n+3)-\ 6\ xx\ 5^(n+1))/(9\ xx\ 5^n-2^...

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  11. Solve the following equations for x\ : (i)\ 7^(2x+3)=1 (ii)\ 2^(x+1)...

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  12. Solve the following equations for x\ : (i)\ 4^(2x)=1/(32) (ii)\ 4^...

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  13. Solve the following equations for x\ : (i)\ 2^(2x)-\ 2^(x+3)+2^4=0 ...

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  14. If 49392=a^4b^2c^3, find the value of a ,\ b\ a n d\ c , where a ,\ b\...

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  15. If 1176=2^a xx\ 3^b xx\ 7^c , and a , b\ a n d\ c are natural numbers...

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

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

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

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

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