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Prove that: (sqrt(3\ xx\ 5^(-3))\ -:r...

Prove that: `(sqrt(3\ xx\ 5^(-3))\ -:root(3)(3^(-1))\ sqrt(5))\ xx\ (3\ xx\ 5^6)^(1/6)\ =3/5`

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

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  2. Simplify: (i)\ ((sqrt(2))/5)^8\ -:((sqrt(2))/5)^(13)

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  3. Prove that: (sqrt(3\ xx\ 5^(-3))\ -:root(3)(3^(-1))\ sqrt(5))\ xx\ ...

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  4. Prove that: 9^(3/2\ )-\ 3\ xx\ 5^0-\ (1/(81))^(-1/2)=15

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  5. Prove that: (1/4)^(-2)-3\ xx\ 8^(2/3)\xx\ 4^0+\ (9/(16))^(-1/2)=(16)/3

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  6. Prove that: (2^(1/2)\ xx\ 3^(1/3)\ xx\ 4^(1/4))/(10^(-1/5)\ xx\ 5^(3/5...

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  7. Prove that: (i)\ sqrt(1/4)+\ (0. 01)^(-1/2)-\ (27)^(2/3)=3/2 (ii)\...

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  8. Prove that: ((64)/(125))^(-2/3)+1/(((256)/(625))^(1/4))+\ ((sqrt(25))/...

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  9. Prove that: (3^(-3)\ xx\ 6^2xx\ sqrt(98))/(5^2\ xx\ root(3)(1/(25))\ x...

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  10. Prove that: ((0. 6)^0-\ (0. 1)^(-1))/((3/8)^(-1)\ (3/2)^3+\ (-1/3)^(-1...

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  11. Solve: 1/(1+x^(a-b))+1/(1+x^(b-a))=?

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  12. Show that : (x^(a(b-c)))/(x^(b(a-c)))÷((x^b)/(x^a))^c=1 ((x^(a+b))^2...

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  13. Solve the following equation - (i) 2^(x+1)=8

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  14. Show that: (i)\ (x^(a-b))^(a+b)\ (x^(b-c))^(b+c)\ (x^(c-a))^(c+a)=1 ...

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  15. Show that: ((a^(x+1))/(a^(y+1)))^(x+y)\ ((a^(y+2))/(a^(z+2)))^(y+z)\ (...

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  16. Show that: ((3^a)/(3^b))^(a+b)\ ((3^b)/(3^c))^(b+c)\ ((3^c)/(3^a))^(c+...

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  17. If 2^x = 3^y =12^z show that 1/z= 1/y+2/x

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  18. If 2^x=3^y=6^(-z) prove that 1/x+1/y+1/z=0

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  19. If a^x=b^y=c^z and b^2=a c , then show that y=(2z x)/(z+x)

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  20. If 3^x=5^y=(75)^z show that z=(xy)/(2x+y

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