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Simplify : ({(a^m)^(1/r)(a^q)^(1/n)}^(nr...

Simplify : `({(a^m)^(1/r)(a^q)^(1/n)}^(nr))/({root(q)(b^n)(root(m)(b))^r}^(mq))*{(a/b)^q}^(-r)`.

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The correct Answer is:
`(a/b)^(mn)`
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CALCUTTA BOOK HOUSE-LAWS OF INDICES-EXERCISE - 6
  1. Simplify : (x^((b+c)/(c-a)))^((1)/(a-b))xx(x^((c+a)/(a-b)))^((1)/(b-c)...

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  2. Simplify : (a+b)^mxx(a-b)^mxx(a^2+b^2)^m.

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  3. Simplify : ({(a^m)^(1/r)(a^q)^(1/n)}^(nr))/({root(q)(b^n)(root(m)(b))^...

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  4. Simpify : (1)/((4x^3-3x)^2)-{((3sqrt(1-x^2))/(x)-((1-x^2)^(3/2))/(x^3)...

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  5. Simplify : (1)/(1+x^(m-n)+x^(m-p))+(1)/(1+x^(n-p)+x^(n-m))+(1)/(1+x^(p...

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  6. Compute the product : (x^n -y^(-n))(x^n +y^(-n)).

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  7. Compute the product : (a^(-m)+b^n)(a^(-2m)-a^(-m)b^n+b^(2n)).

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  8. Compute the division : (a^(3^n)-b^(3^n))/(a^(3^(n-1))-b^(3^(n-1))).

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  9. Compute the division : (x^3-y^2)+(x^(1/2)-y^(1/3)).

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  10. Rearrange according to the ascending values : 3^(1/2),4^(1/3),5^(1/4).

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  11. Rearrange according to the ascending values : 2^(18),3^(12),4^(24),5^(...

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  12. Prove that : If (4.44)^x=(0.444)^y=1000, then prove that (1)/(x)-(1)/(...

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  13. If (111.1)^x=(11.11)^y=(1.111)^z then prove that (1)/(x)-(2)/(y)+(1)/(...

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  14. If 2^a=3^b=6^(-c), then prove that (1)/(a)+(1)/(b)+(1)/(c )=0.

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  15. If x^a=y^b=z^c " and "y^3=zx, then prove that b(c+a)=3ca.

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  16. If 4^a=36^b =9^c, then prove that (b)/(a)+(b)/( c)=1.

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  17. If x^2=y^3, then prove that (x/y)^(3/2)+(y/x)^-(2/3)=x^(1/2)+y^(1/3).

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  18. If a^x=z^y" and "a^z=z^x, then prove that x^2 =yz.

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  19. If (x^(n^2))^n = (x^(2^n))^2, then show that root(n+1)(n^3)=2.

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  20. If x=(sqrt(2)+1)^(-1/3), then prove that (x-x^(-1))^3+3(x-x^(-1))+2=0.

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