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Simplify each of the following by removi...

Simplify each of the following by removing radical signs and negative indices wherever they occur: `(i)\ (sqrt(4))^(-3/4)` ` (ii)\ (sqrt(5))^(-3)\ xx\ (sqrt(2))^(-3)` ` (iii)1/((4^(-5)) 3)`

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Simplify each of the following by removing radical signs and negative indices wherever they occur: (i)\ (sqrt(4))^(-7)\ xx\ \ (sqrt(2))^(-5)

Evaluate each of the following by removing radical signs and negative indices wherever they occur: (i) (27)^(-2/3) (ii) ((64)/(25))^(-3/2)

Evaluate each of the following by removing radical signs and negative indices wherever they occur: (i)\ (64)^(1/3) (ii) (125)^(-1/3) (iii)\ (27)^(-2/3) (iv) ((64)/(25))^(-3/2)

Evaluate each of the following removing radical sign and negative indices wherever they occur (i) (64)^(1/3) (ii) (125)^(-1/3) (iii) (27)^(-2/3) (iv) (64/25)^(-3/2) (v) (-1/2)^(-5) (vi) (1/4)^(-1) (vii) 5^(-2)

Simplify the following (3+sqrt(2))(4+sqrt(7))

Simplify each of the following by rationalising the denominator; 1/(5+sqrt(2)) (ii) (5+sqrt(6))/(5-sqrt(6)) (iii) (7+3sqrt(5))/(7-3sqrt(5)) (iv) (2sqrt(3)-sqrt(5))/(2sqrt(2)+3sqrt(3))

Simplify each of the following by rationalising the denominator: (7+3sqrt(5))/(7-3sqrt(5)) (ii) (2\ sqrt(3)-\ sqrt(5))/(2sqrt(2)+\ 3sqrt(3))

Simplify: (i) (5+\ sqrt(5))\ (5-\ sqrt(5)) (ii) (3+2sqrt(2))\ (3-2sqrt(2))

Rationalize the denominator of : (i) (2sqrt(3))/sqrt(5)" (ii) "1/(sqrt(3)-sqrt(2))

Factorise: (i) 4sqrt(3)x^(2) + 5x-2sqrt(3) (ii) 7sqrt(2)x^(2)-10x - 4sqrt(2)

RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. Simplify : ((25)^(3/2)*(243)^(3/5))/((16)^(5/4)*(8)^(4/3))

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

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

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

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

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

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

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

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  9. 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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  10. 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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  11. If x=3,\ find the value of (x^(1/3)+\ x^(-1/3))\ (x^(2/3)+x^(-2/3)-1\...

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

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

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

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  15. Solve the equation for x : 2^3(5^0+3^(2x))=\ 8 8/(27)

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  16. Solve the equation: 3(2^x+1)-2^(x+2)+5=0

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  17. Solve the equations for x\ a n d\ y: 3^x=9\ xx\ 3^y ,\ 8\ xx\ 2^y=4^x

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  18. Solve the equation for x\ a n d\ y (32)^x-:2^(y+1)=1,\ 16^(4-x/2)-8^y...

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  19. If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

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  20. If a^x=b^y=c^z\ a n d\ b^2=a c , prove that y=(2x z)/(x+z)

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