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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))(x^(c+a))^2)/((x^a x^b x^c)^4)=1`

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To show that \[ \frac{x^{a(b-c)}}{x^{b(a-c)}} \cdot \left(\frac{x^b}{x^a}\right)^c = 1 \] and ...
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Show that: (x^(a(b-c)))/(x^(b(a-c)))-:((x^(b))/(x^(a)))^(c)=1((x^(a+b))(x^(b+c))^(2)(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))=1

Prove that. (i) sqrt(x^(-1) y) .sqrt(y^(-1) z) . Sqrt(z^(-1) x) = 1 (ii) ((1)/(x^(a-b)))^((1)/(a-c)).((1)/(x^(b-c))).((1)/(x^(c-b)))^((1)/(c-b))= 1 (iii) (x^(a(b-c)))/(x^(b(a-c))) div ((x^(b))/(x^(a))) (iv) ((x^(a+b))^(2)(x^(b+c))^(2)(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))

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

Prove that: ((x^(a+b))^(2)(x^(b+c))^(2)(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))

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

Show that (x^(a+b))^(a-b)times(x^(b+c))^(b-c)times(x^(c+a))^(c-a)=1

Prove that: ((x^(a))/(x^(b)))^(c)x((x^(b))/(x^(c)))^(a)x((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)))^((1)/(ab))((x^(b))/(x^(c)))^((1)/(bc))((x^(c))/(x^(a)))^((1)/(ac))=1

RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
  1. Prove that : (a^(-1))/(a^(-1)+b^(-1))+(a^(-1))/(a^(-1)-b^(-1))=(2b^2)/...

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

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

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  4. If (9^nxx3^2xx(3^(-n/2))^(-2)-(27)^n)/(3^(3m)xx2^3)=1/(27), Prove th...

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

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

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  7. Evaluate each of the following: (i)5^2*5^4 (ii) 5^8+5^3 (iii) (3...

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  8. Evaluate each of the following: (i)(2/(11))^4*((11)/3)^2*(3/2)^3 (ii...

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  9. If a=2 and b=3, then find the values of each of the following: a^a+b^b...

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  10. Assuming that x , y are positive real numbers, simplify each of the fo...

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  11. Simplify : ((25)^(3/2)x(243)^(3/5))/((16)^(5/4)x(8)^(4/3))

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  12. Simplify: ((81)/(16))^(-3/4)xx[((25)/9)^(-3/2)-:(5/2)^(-3)]

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  13. If x , y ,z are positive real numbers show that: sqrt(x^(-1)y)dotsqrt(...

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  14. Evaluate each of the following 5^2\xx\ 5^4 (ii) (3^2)^3 ​ ​ ​

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  15. Evaluate each of the following (i)((11)/(12))^3 (ii) (3/4)^(-3)

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  16. Evaluate each of the following: (i) (2/(11))^4 xx ((11)/3)^2 xx (3/2)...

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  17. Evaluate each of the following: (i)\ 2^(55)xx\ 2^(60)-\ 2^(97)xx\ 2^(...

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  18. If a=2 and b=3 , then find the values of each of the following: a^a+b^...

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  19. If a=2 and b=3 , then find the values of each of the following: (a/b)^...

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  20. Simplify the following (ii)(3a^4b^3)(18 a^3b^5) (ii) (3a^7b^6)/(18 ...

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