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

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

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`[{(625)^(-1/4)}^(-1/2)]^2`
Solving the powers,
`-1/2 xx -1/2 xx 2=1/4`
Now,
`(625)^(1/4)=(5^4)^(1/4)=5`
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(625)^(-3/4)

[(625)^(-1/2)]^(-1/4)

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)

(((625)^(-1//2))^(-1//4))^(2)=

Simplify sqrt(25)/(64)^(1/3)+(256/625)^(-1/4)+1/(64/125)^(2/3)

Simplify: [(2 10/27))^(-2/3) ÷ (11 1/9))^(-0.5)] +[(6.25)^(0.5) ÷ (-4)^(-1)]

Prove that . (i) [8^(-(2)/(3)) xx 2^((1)/(2))xx 25^(-(5)/(4))] div[32^(-(2)/(5)) xx 125 ^(-(5)/(6)) ] = sqrt(2) (ii) ((64)/(125))^(-(2)/(3)) = (1)/(((256)/(625))^((1)/(4)))+ (sqrt(25))/(root3(64)) = (65)/(16) (iii) [7{(81)^((1)/(4)) +(256)^((1)/(4))}^((1)/(4))]^(4) = 16807 .

(64/125)^(-2/3)+(256/625)^(-1/4)+(3/7)^0=

((16)^((1)/(4)))/((27)^((1)/(3)))+((625)^((1)/(4)))/((81)^((1)/(4)))-(1)/((243)^((1)/(5)))=2

(1) Simplify (1)/((27)^(-(1)/(3)))+(1)/((625)^(-(1)/(4)))*(2) find the smallest of the numbers 6^((1)/(3)),24(1)/(4),8^((1)/(4))

RD SHARMA-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)xx(243)^(3/5))/((16)^(5/4)xx(8)^(4/3)) (16xx 2^(n...

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  8. Simplify: ((81)/(16))^(-3/4)xx[((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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  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) and y= 27^(1/3) find the value of x+y-1/(x^2+x y+y^2)

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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 3=(0. 6)^(3-2x)

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