Home
Class 9
MATHS
Simplify: (i)\ (16^(-1/5))^(5/2) (ii...

Simplify: `(i)\ (16^(-1/5))^(5/2)` `(ii)\ (32)^(-3/5)` `(iii)\ (343)^(-2/3)`

Text Solution

Verified by Experts

(i) `(16^(-1/5))^(5/2)`
`=16^((-1/5xx5/2))`
`=16^(-1/2)`
`=4^((2xx-1/2))`
`=1/4`

(ii) `32^(-3/5)`
`=2^((5xx-3/5))`
`=2^(-3)`
`=1/8`

(iii) `343^(-2/3)`
`=7^((3xx-2/3))`
`=7^(-2)`
`=1/49`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE GEOMETRY

    RD SHARMA|Exercise All Questions|23 Videos
  • FACTORIZATION OF ALGEBRAIC EXPRESSIONS

    RD SHARMA|Exercise All Questions|226 Videos

Similar Questions

Explore conceptually related problems

Simplify (i) ((81)/(49))^(-(3)/(2)) (ii) (14641)^(0.25) (iii) ((32)/(243))^(-(4)/(5)) (iv) ((7776)/(243))^(-(3)/(5))

(i) 6x^(-2) (ii) (1)/(5)x^(5) (iii) (1)/(3x)

Simplify (i) (6^(1//4))/(6^(1//5)) (ii) (8^(1//2))/(8^(2//3)) (iii) (5^(6//7))/(5^(2//3))

Simplify : (i) ((243)/(32))^((4)/(5)) (ii) root(3)((343)^(-2))

Find : (i) 9^(3//2) (ii) 32^(2//5) (iii) 16^(3//4) (iv) 125^(-1//3)

Find : (i) 64^(1//2) (ii) 32^(1//5) (iii) 125^(1//3)

Simplify (i) 2^(2/3). 2^(1/3) (ii) (3^(1/5))^4 (iii) (7^(1/5))/(7^(1/3)) (iv) 13^(1/5). 17^(1/5)

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)

Simplify: (-3)^2xx((-5)/(12))^2 (ii) ((-2)/5)^3-:((-3)/(10))^4

Simplify: (3/4)^2 (ii) ((-2)/3)^4 (iii) ((-4)/5)^5

RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
  1. Assuming that x ,\ y ,\ z are positive real numbers, simplify each of ...

    Text Solution

    |

  2. Assuming that x ,\ y ,\ z are positive real numbers, simplify each of ...

    Text Solution

    |

  3. Simplify: (i)\ (16^(-1/5))^(5/2) (ii)\ (32)^(-3/5) (iii)\ (343...

    Text Solution

    |

  4. Simplify: (i)\ (0. 001)^(1/3) (ii)\ ((25)^(3/2)\ xx\ (243)^(3/5))/...

    Text Solution

    |

  5. Simplify: (i)\ ((sqrt(2))/5)^8\ -:((sqrt(2))/5)^(13) (ii)\ ((5^(-1...

    Text Solution

    |

  6. Prove that: (sqrt(3\ xx\ 5^(-3))\ -:root(3)(3^(-1))\ sqrt(5))\ xx\ ...

    Text Solution

    |

  7. Prove that: 9^(3/2\ )-\ 3\ xx\ 5^0-\ (1/(81))^(-1/2)=15

    Text Solution

    |

  8. Prove that: (1/4)^(-2)-3\ xx\ 8^(2/3)\xx\ 4^0+\ (9/(16))^(-1/2)=(16)/3

    Text Solution

    |

  9. Prove that: (2^(1/2)\ xx\ 3^(1/3)\ xx\ 4^(1/4))/(10^(-1/5)\ xx\ 5^(3/5...

    Text Solution

    |

  10. Prove that: (i)\ sqrt(1/4)+\ (0. 01)^(-1/2)-\ (27)^(2/3)=3/2 (ii)\...

    Text Solution

    |

  11. Prove that: ((64)/(125))^(-2/3)+1/(((256)/(625))^(1/4))+\ ((sqrt(25))/...

    Text Solution

    |

  12. Prove that: (3^(-3) xx 6^2xx sqrt(98))/(5^2 xx root(3)(1/(25)) xx (15)...

    Text Solution

    |

  13. Prove that: ((0. 6)^0- (0. 1)^(-1))/((3/8)^(-1) (3/2)^3+ (-1/3)^(-1))=...

    Text Solution

    |

  14. 1/(1+x^(a-b))+1/(1+x^(b-a))=?

    Text Solution

    |

  15. Show that : (x^(a(b-c)))/(x^(b(a-c)))/((x^b)/(x^a))^c=1 ((x^(a+b))^...

    Text Solution

    |

  16. Show that: (i)\ (x^(a-b))^(a+b)\ (x^(b-c))^(b+c)\ (x^(c-a))^(c+a)=1 ...

    Text Solution

    |

  17. Show that:(a^(x-y))^(x+y).(a^(y-z))^(y+z).(x^(z-x))^(z+x)=1

    Text Solution

    |

  18. Show that: ((3^a)/(3^b))^(a+b)\ ((3^b)/(3^c))^(b+c)\ ((3^c)/(3^a))^(c+...

    Text Solution

    |

  19. If 2^x = 3^y =12^z show that 1/z= 1/y+2/x ​ ​

    Text Solution

    |

  20. If 2^x=3^y=6^(-z) prove that 1/x+1/y+1/z=0

    Text Solution

    |