Home
Class 9
MATHS
If x is a positive real number and the e...

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`

Promotional Banner

Topper's Solved these Questions

  • INDICES [EXPONENTS]

    ICSE|Exercise EXERCISE 7 (C)|19 Videos

  • INDICES [EXPONENTS]

    ICSE|Exercise EXERCISE 7 (A)|23 Videos

  • INDICES (EXPONENTS)

    ICSE|Exercise 4 Marks Questions|9 Videos

  • INEQUALITIES

    ICSE|Exercise EXERCISE 11|42 Videos

Similar Questions

Explore conceptually related problems

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^a)/(x^b))^(1/(a b))\ ((x^b)/(x^c))^(1/(b c))\ \ ((x^c)/(x^a))^(1/(a c))=1

If x is a positive real number and the exponents are rational numbers, Find: ((x^a)/(x^b))^(a^2+b^2-a b). ((x^b)/x^c)^(b^2+c^2-b c). ((x^c)/(x^(a)))^(c^2+a^2-c a)

Assuming that x is a positive real number and a ,\ b ,\ c are rational numbers, show that: ((x^a)/(x^b))^(a^2+a b+b^2)((x^b)/(x^c))^(b^2+b c+c^2)((x^c)/(x^a))^(c^2+c a+a^2)=1

Prove that: ((x^a)/(x^b))^c\xx\ ((x^b)/(x^c))^a\ xx\ ((x^c)/(x^a))^b=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

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)

(x^a/x^b)^(a+b).(x^b/x^c)^(b+c).(x^c/x^a)^(c+a)

Show that: (i) (x^(a(b-c)))/(x^(b(a-c)))-:((x^b)/(x^a))^c=1,

Prove that: ((x^a)/(x^b))^(a^(2+a b+b^(2)))xx\ ((x^b)/(x^c))^(b^(2+b c+c^2))\ xx\ ((x^c)/(x^a))^(c^(2+c a+a^2))

ICSE-INDICES [EXPONENTS]-EXERCISE 7 (B)
  1. Solve : 3^(x2) : 3^(x) = 9 : 1

    Text Solution

    |

  2. Solve : 8 xx 2^(2x) + 4 xx 2^(x +1) = 1 + 2^(x)

    Text Solution

    |

  3. Solve : 2^(2x) + 2^(x+2) - 4 xx 2^(3) = 0

    Text Solution

    |

  4. Solve : (sqrt(3))^(x-3)=(sqrt(3))^((x+1)/4)

    Text Solution

    |

  5. Find the values of m and n if : 4^(2m)=(root(3)(16))^(-(6)/(n))=(sqr...

    Text Solution

    |

  6. Solve for x and y if : (sqrt(32))^(x)÷2^(y+1)= 1 and 8^(y)-16^(4-(x)...

    Text Solution

    |

  7. If x is a positive real number and the exponents are rational numbe...

    Text Solution

    |

  8. Show that : (x^(a(b-c)))/(x^(b(a-c)))÷((x^b)/(x^a))^c=1 ((x^(a+b))^2...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. If 5^(-p)=4^(-q)=20^(r ). Show that (1)/(p)+(1)/(q)+(1)/(r )=0

    Text Solution

    |

  12. If m =! n and (m + n)^(-1) (m^(-1) + n^(-1)) = m^(x) n^(y), show that ...

    Text Solution

    |

  13. If 5^(x +1) = 25^(x-2), find the value of 3^(x-3) xx 2^(3-x).

    Text Solution

    |

  14. If 4^(x+3)=112+8xx4^(x), find (18x)^(3x)

    Text Solution

    |

  15. Solve for x : 4^(x-1)xx(0.5)^(3-2x)=((1)/(8))^(-x)

    Text Solution

    |

  16. Solve for x : (a^(3x+5))^(2) . (a^(x))^(4) = a^(8x+12).

    Text Solution

    |

  17. Solve for x : (81)^((3)/(4))-((1)/(32))^(-(2)/(5))+x((1)/(2))^(-1).2^(...

    Text Solution

    |

  18. Solve for x : 2^((3x + 3)) = 2^((3x + 1)) + 48.

    Text Solution

    |

  19. Solve for x : 3(2^(x) + 1) - 2^(x + 2)) + 5 = 0.

    Text Solution

    |

  20. Solve for x : 9^(x + 2)) = 720 + 9^(x)

    Text Solution

    |