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[{(625)^(-1/4)}^(-1/2)]^2...

`[{(625)^(-1/4)}^(-1/2)]^2`

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simplify (i) (1^(3)+2^(3)+3^(3))^(1/2) (ii) (3/5)^(4)(8/5)^(-12)(32/5)^(6) ,(iii) (1/27)^(-2/3) (vi) [((625)^(-1/2)))^(-1/4)]^(2) ,(v) (9^(1/3)xx27^(-1/2))/(3^(1/6)xx3^(-2/3)) (vi) 64^(-1/3)[64^(1/3)-64^(2/3)] (8^(1/3)xx16^(1/3))/(32^(-1/3)

Solve : {(625^(-(1)/(2))) ^(-(1)/(4))}=(0.2)^(4-3x)

Express each of the following as a rational number of the form p/q : (i) (2^(-1)+3^(-1))^2 (ii) (2^(-1)-4^(-1))^2 ] (iii) {(3/4)^(-1)-(1/4)^(-1)}^(-1)

Find the values of each of the following : (1/2)^(-1)+\ (1/3)^(-1)+\ (1/4)^(-1) (1/2)^(-2)+\ (1/3)^(-2)+(1/4)^(-2)

Simplify each of the following: (i)\ (625)^(-1/4) (ii)\ ((256)/(81))^(5/4)

lim_(x->a){[(a^(1/2)+x^(1/2))/(a^(1/4)-x^(1/4)))^(- 1)-(2(a x)^(1/4))/(x^(3/4)-a^(1/4)x^(1/2)+a^(1/2)x^(1/4)-a^(3/4))]^(- 1)-sqrt2^(log_4 a)}^8

Simplify : (1/4)^(-2)+\ (1/2)^(-2)+(1/3)^(-2)

Evaluate each of the following : (i){(81)^(1//5)}^(5//2)" "(ii)(3sqrt(64))^(-2)" "(iii)9^(3//2)+3xx4^(0)-((1)/(81))^(-1//2) (vi)sqrt((1)/(9))+(0.01)^(-1//2)-(27)^(4//3)" "(v)((125)/(64))^(2//3)+((256)/(625))^(-1//4)

A : (1)/(2)-(1)/(2).(1)/(2^(2))+(1)/(3).(1)/(2^(3))-(1)/(4).(1)/(2^(4))+....=log_(e)((3)/(2)) R : log_(e)(1+x)=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+...

int((x^(- 6)-64)/(4+2x^(- 1)+x^(- 2))*(x^2)/(4-4x^(- 1)+x^(- 2))-(4x^2(2x+1))/(1-2x))dx

RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. Simplify each of the following: (i)\ (625)^(-1/4) (ii)\ ((256)/(81)...

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  2. Simplify each of the following: (i)\ ((243)/(32))^(-4/5) (ii)\ (32...

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  3. [{(625)^(-1/4)}^(-1/2)]^2

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  4. Simplify: (256)^-(4^(((-3)/2)))

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  5. Simplify: 4/((216)^(-2/3))+1/((256)^(-3/4))+2/((243)^(-1/5))

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  6. Simplify: sqrt(1/4)+(0. 01)^(-1/2)-(27)^(2/3)

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  7. Simplify : ((25)^(3/2)*(243)^(3/5))/((16)^(5/4)*(8)^(4/3))

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

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  9. Simplify each of the following by removing radical signs and negative ...

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  10. Simplify each of the following by removing radical signs and negative ...

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  11. Assuming that x , y , z are positive real numbers, simplify each of th...

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  12. Assuming that x , y , z are positive real numbers, simplify each of th...

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  13. Assuming that x , y , z are positive real numbers, simplify each of th...

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

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  15. If ((x^(-1)y^2)/(x^3y^(-2)))^1.\ ((x^6\ y^(-3))/(x^2\ y^3))^(1/2)=x^a ...

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  16. If x=\ 28^(1/3)\ \ a n d\ y=\ 27^(1/3) find the value of x-y-1/(x^2+x...

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  17. If x=3,\ find the value of (x^(1/3)+\ x^(-1/3))\ (x^(2/3)+x^(-2/3)-1\...

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  18. If 25^(n-1) + 100 = 5^ (2n-1), find the value of n :

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  19. Solve the equation for x : (i)\ 4^(2x)=1/(32) (ii)\ sqrt((3/5)^(1-...

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  20. Solve the equation for x : (5^0+2/3)^2 =(0. 6)^(3-2x)

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