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

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

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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

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

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^b)/(x^c))^a\ ((x^c)/(x^a))^b\ ((x^a)/(x^b))^c=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

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))

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

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

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))

RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. If x is a positive real number and the exponents are rational numbe...

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  2. If x is a positive real number and the exponents are rational number...

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

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

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  5. 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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  6. Prove that: (a^(-1))/(a^(-1)+b^(-1))+(a^(-1))/(a^(-1)-b^(-1))=(2b^2)/(...

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  7. If a ,\ b ,\ c are distinct positive prime integers such that a^2b^3c^...

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  8. Find the value of x , if 5^(x-3)\ 3^(2x-8)=225

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  9. Solve the following equations: (i) 2^(x-5)=256 (ii) 2^(x+3)=4^(x-...

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  10. If 9^(x+2)=720+9^x , find the value of (4x)^(1/x)

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  11. Solve the equation for x: 2^(2x+1)=17. 2^x-2^3

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  12. Solve the equation for x: 5^(2x+1)=6. 5^x-1

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  13. Simplify the following: 3(a^4b^3)^10xx5(a^2b^2)^3

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  14. Simplify that: (2x^(-2)y^3)^3

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  15. Simplify that: ((4\xx\ 10^7)(6\ xx\ 10^(-5)))/(8\ xx\ 10^4)

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  16. Simplify that: (4a b^2\ (-5a b^3))/(10 a^2b^2)

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  17. Simplify that : ((x^2\ y^2)/(a^2b^3))^n

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  18. Simplify that: ((a^(2n-9))^6)/(a^(2n-4))

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  19. If a=3\ \ a n d\ b=-2\ , find the values of: (i)\ a^a+b^b (ii)\ a^b+b...

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  20. 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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