Home
Class 9
MATHS
For any positive real number x;write the...

For any positive real number x;write the value of `{(x^a)^b}^(1/(ab)) {(x^b)^c}^(1/(bc)) {(x^c)^a}^(1/(ca))`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COORDINATE GEOMETRY

    RD SHARMA ENGLISH|Exercise All Questions|23 Videos

  • FACTORIZATION OF ALGEBRAIC EXPRESSIONS

    RD SHARMA ENGLISH|Exercise All Questions|226 Videos

Similar Questions

Explore conceptually related problems

For any positive real number x , find the value of ((x^a)/(x^b))^(a+b)\ xx\ ((x^b)/(x^c))^(b+c)\ xx\ ((x^c)/(x^a))^(c+a)

Assuming that x is a positive real number and a ,\ b ,\ c are rational numbers, show that: ((x^a)/(x^b))^(1/(a b))\ ((x^b)/(x^c))^(1/(b c))\ \ ((x^c)/(x^a))^(1/(a c))=1

If a, b, c are positive real numbers, then the least value of (a+b+c)((1)/(a)+(1)/(b)+(1)/( c )) , is

If a, b, c are three distinct positive real numbers, then the least value of ((1+a+a^(2))(1+b+b^(2))(1+c+c^(2)))/(abc) , is

If x is a positive real number and the exponents are rational numbers, show that: ((x^a)/(x^b))^(a+b-c)\ ((x^b)/(x^c))^(b+c-a)((x^c)/(x^a))^(c+a-b)=1

Ifa, b, c are positive real number such that ab^(2)c^(3) = 64 then minimum value of ((1)/(a) + (2)/(b) + (3)/(c)) is equal to

Assuming that x is a positive real number and a ,\ b ,\ c are rational numbers, show that: ((x^a)/(x^b))^(a+b)\ ((x^b)/(x^c))^(b+c)((x^c)/(x^a))^(c+a)=1

Assuming that x is a positive real number and a ,\ b ,\ c are rational numbers, show that: ((x^b)/(x^c))^a\ ((x^c)/(x^a))^b\ ((x^a)/(x^b))^c=1

If a+b+c=1 , the greatest value of (ab)/(a+b)+(bc)/(b+c)+(ca)/(c+a) , is

(x^(1/(a-b)))^(1/(a-c))xx(x^(1/(b-c)))^(1/(b-a))xx(x^(1/(c-a)))^(1/(c-b))

RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. For any positive real number x , find the value of ((x^a)/(x^b))^(a+b)...

    Text Solution

    |

  2. Write the value of {5"("8^(-1/2)"}"^(-1/4)}^2

    Text Solution

    |

  3. For any positive real number x;write the value of {(x^a)^b}^(1/(ab)) {...

    Text Solution

    |

  4. If (x-1)^3=8, what is the value of (x+1)^2\ ?

    Text Solution

    |

  5. If 2^4\ xx\ 4^2=16^x , then find the value of x ?

    Text Solution

    |

  6. If 3^(x-1)=9 and 4^(y+2)=64 , what is the value of x/y\ ?

    Text Solution

    |

  7. Write the value of root(3)(7)\ xx\root(3)( 49)

    Text Solution

    |

  8. Write (1/9)^(-1/2)\ xx\ (64)^(-1/3) as a rational number.

    Text Solution

    |

  9. Write the value of root(3)(125)\ xx\ root(3)(27)

    Text Solution

    |

  10. The value of {2-3(2-3)^3}^3 is (a)5 (b) 125 (c) 1/5 (d) -12...

    Text Solution

    |

  11. Which one is the correct option (256)^(0. 16)xx(256)^(0. 09)=? a. 4...

    Text Solution

    |

  12. If 10^(2y)=\ 25\ , then 10^(-y) equals (a)-1/5 (b) 1/(50) (c)...

    Text Solution

    |

  13. The value of x-y^(x-y) when x=2 and y=-2 is (a)18 (b) -18\ (c...

    Text Solution

    |

  14. The product of the square root of x with the cube root of x is (a) cub...

    Text Solution

    |

  15. if 9^(x+2)=240+9^x , then x= (a)0. 5 (b) 0.2 (c) 0.4 (d) 0.1

    Text Solution

    |

  16. The seventh root of x divided by the eighth root of x is (a)x (b) ...

    Text Solution

    |

  17. The square root of 64 divided by the cube root of 64 is (a)64 (b...

    Text Solution

    |

  18. Which of the following is (are) not equal to {(5/6)^(1/5)}^(-1/6)\ ? ...

    Text Solution

    |

  19. When simplified (x^(-1)+y^(-1))^(-1) is equal to (a)\ x y (b) x+y...

    Text Solution

    |

  20. If 8^(x+1)=64 , what is the value of 3^(2x+1) ? (a)1 (b) 3 (c) 9 ...

    Text Solution

    |