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If a^m a^n =a^(mn), then express m in te...

If `a^m a^n =a^(mn)`, then express m in terms of n.

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The correct Answer is:
`m= (n)/(n-1)`
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CALCUTTA BOOK HOUSE-LAWS OF INDICES-EXERCISE - 6
  1. If p=a^x,q=a^y" and "a^2=(p^yq^x)^z, then find the value of xyz.

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  2. If a^(m^n)= (a^m)^n, then express m in terms of n.

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  3. If a^m a^n =a^(mn), then express m in terms of n.

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  4. If x=2,y=4, then what is the value of x+2y+sqrt((x-2y)^2)?

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  5. Which one is the greatest ? 3^(2^(2^2)), 3^(2.2.2), 3.2.2.2.

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  6. Find the value of root(3)(x^4sqrt(x^(-5)sqrt(x^6))).

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  7. Calculate : ((1)/(81))^(-5/4).

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  8. Calculate : {root(3)(4)xx(1)/(root(6)(8))xxroot(12)(2^(-1))}^(3/4).

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  9. Simplify : x^(1/3).x^(-1/4).x^(-1/2) divx^(-(7)/(12))

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  10. Simplify : root(4)(a^2b^3c^4)xxroot(3)(a^4b^6)xx(a^(1/2)b^(1/3)c^(1/4)...

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  11. Simplify : {(a)^(n^(2)-1)}^((n)/(n+1))xx(sqrt(a^(2n)))/(a).

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  12. Simplify : ((p+(1)/(q))^m(p-(1)/(q))^n)/((q+(1)/(p))^m(q-(1)/(p))^n).

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  13. Simplify : (2^n.6^(m+1).10^(m-n).15^(m+n-2))/(4^m.3^(m+n).25^(m-1)).

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  14. Simplify : (x^((b+c)/(c-a)))^((1)/(a-b))xx(x^((c+a)/(a-b)))^((1)/(b-c)...

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

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

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

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

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

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