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Prove that: (2^(1/2)\ xx\ 3^(1/3)\ xx\ 4...

Prove that: `(2^(1/2)\ xx\ 3^(1/3)\ xx\ 4^(1/4))/(10^(-1/5)\ xx\ 5^(3/5))\ -:(3^(4/3)\ xx\ 5^(-7/5))/(4^(-3/5)\ xx\ 6)=10`

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To prove that \[ \frac{2^{1/2} \cdot 3^{1/3} \cdot 4^{1/4}}{10^{-1/5} \cdot 5^{3/5}} - \frac{3^{4/3} \cdot 5^{-7/5}}{4^{-3/5} \cdot 6} = 10, \] we will simplify both sides step by step. ...
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(2^((1)/(2))xx3^((1)/(3))xx4^((1)/(4)))/(10^(-(1)/(5))xx5^((3)/(5)))-:(3^((4)/(3))xx5^(-(7)/(5)))/(4^(-(3)/(5))xx6)=10

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RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
  1. Prove that: 9^(3/2\ )-\ 3\ xx\ 5^0-\ (1/(81))^(-1/2)=15

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

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

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

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

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  6. Prove that: (3^(-3) xx 6^2xx sqrt(98))/(5^2 xx root(3)(1/(25)) xx (15)...

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

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  8. 1/(1+x^(a-b))+1/(1+x^(b-a))=?

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

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

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  11. Show that:(a^(x-y))^(x+y).(a^(y-z))^(y+z).(x^(z-x))^(z+x)=1

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

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

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

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

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

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  17. If 27^x=9/(3^x), find xdot

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  18. Find the values of x in each of the following : (i)2^(5x)-:2^x=25^(2...

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  19. Find the value of x in each of the following: (i)\ (3/5)^x\ (5/3)^(2x)...

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  20. Find the value of x in each of the following: (i)2^(x-7) xx 5^(x-4)=1...

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