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Show that : (x^(a(b-c)))/(x^(b(a-c)))÷((...

Show that : `(x^(a(b-c)))/(x^(b(a-c)))÷((x^b)/(x^a))^c=1` `((x^(a+b))^2(x^(b+c))^2 (x^(c+a))^2)/((x^a x^b x^c)^4)=1`

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Show that : (i) x^(a(b-c))/(x^(b(a-c)))/((x^b)/(x^a))^c=1 , (ii) ((x^(a+b))^2(x^(b+c))^2(x^(c+a))^2)/((x^a x^b x^c)^4)=1

Show that: (i) (x^(a(b-c)))/(x^(b(a-c)))-:((x^b)/(x^a))^c=1,

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

Show that: (i)\ (x^(a-b))^(a+b)\ (x^(b-c))^(b+c)\ (x^(c-a))^(c+a)=1 (ii)\ {(x^(a-a^(-1)))^(1/(a-1))}^(a/(a+1))=x

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

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))

(x^(1/(a-b)))^(1/(a-c))xx(x^(1/(b-c)))^(1/(b-a))xx(x^(1/(c-a)))^(1/(c-b))

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

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))

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

RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. Prove that: ((0. 6)^0-\ (0. 1)^(-1))/((3/8)^(-1)\ (3/2)^3+\ (-1/3)^(-1...

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

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

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

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

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

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

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

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

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

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

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

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  13. Find the values of x in each of the following : (i)2^(5x)-:2^x=2^(20/...

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

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  15. Find the value of x in each of the following: 2^(x-7)\ xx\ 5^(x-4)=125...

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  16. Find the value of x in each of the following: (i)\ 5^(2x+3)=1 (ii)\ ...

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  17. If x=2^(1/3)+\ 2^(2/3) show that x^3-6x=6

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  18. Determine (8x)^x , if 9^(x+2)=240+9^x

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  19. If 3^(x+1)=9^(x-2), find the value of 2^(1+x)

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  20. If 3^(4x)=(81)^(-1) and 10^(1/y)=0. 0001 , find the value of 2^(-x+4y)

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