Home
Class 9
MATHS
If a ,\ b ,\ c are distinct positive pri...

If `a ,\ b ,\ c` are distinct positive prime integers such that `a^2b^3c^4=49392 ,\ ` find the value of `a ,\ b\ ` and `c`

Text Solution

Verified by Experts

By prime factorization, we get rewrite `49392`,
`49392=2xx2xx2xx2xx3xx3xx7xx7xx7`
`49392=2^4xx3^2xx7^3`

On comparing the factorized form with `a^2b^3c^4`
we get,
`a^2b^3c^4=2^4xx3^2xx7^3`
If,
`a=3, b=7 and c=2`
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

If a and b are distinct positive primes such that a^(6)b^(-4)3=a^(x)b^(2y), find x and y.

If a,b,c,d are distinct integers in an A.P. such that d=a^(2)+b^(2)+c^(2), then find the value of a+b+c+d

If a, b, c are distinct positive integers such that ab+bc+cage74 , then the minimum value of a^(3)+b^(3)+c^(3)-3abc, is

If a and b be positive integers such that a^2-b^2=19 , then the value of a is 9 (b) 10 (c) 19 (d) 20

If a,b,c are positive real numbers such that a +b+c=18, find the maximum value of a^(2)b^(3)c^(4)

If a,b,c,d are distinct integers in A.Puch that d=a^(2)+b^(2)+c^(2), then a+b+c+d is

RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
  1. If a b c=1, show that 1/(1+a+b^(-1))+1/(1+b+c^(-1))+1/(1+c+a^(-1))=1

    Text Solution

    |

  2. Prove that: (a^(-1))/(a^(-1)+b^(-1))+(a^(-1))/(a^(-1)-b^(-1))=(2b^2)/(...

    Text Solution

    |

  3. If a ,\ b ,\ c are distinct positive prime integers such that a^2b^3c^...

    Text Solution

    |

  4. Find the value of x , if 5^(x-3)\xx\ 3^(2x-8)=225

    Text Solution

    |

  5. Solve the following equations: 2^(x-5)=256 (ii) 2^(x+3)=4^(x-1)

    Text Solution

    |

  6. If 9^(x+2)=720+9^x , find the value of (4x)^(1/x)

    Text Solution

    |

  7. Solve the equation for x: 2^(2x+1)=17. 2^x-2^3

    Text Solution

    |

  8. Solve the equation for x 5^(2x+1)=6. 5^x-1

    Text Solution

    |

  9. 3(a^4b^3)^10xx5(a^2b^2)^3

    Text Solution

    |

  10. Simplify that: (2x^(-2)y^3)^3

    Text Solution

    |

  11. Simplify that: ((4\xx\ 10^7)(6\ xx\ 10^(-5)))/(8\ xx\ 10^4)

    Text Solution

    |

  12. Simplify that: (4a b^2\ (-5a b^3))/(10 a^2b^2)

    Text Solution

    |

  13. Simplify that : ((x^2\ y^2)/(a^2b^3))^n

    Text Solution

    |

  14. Simplify that: ((a^(2n-9))^6)/(a^(2n-4))

    Text Solution

    |

  15. If a=3 and b=-2, find the values of: (i)\ a^a+b^b (ii)\ a^b+b^a (iii...

    Text Solution

    |

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

    Text Solution

    |

  17. Prove that: ((x^a)/(x^b))^c\xx\ ((x^b)/(x^c))^a\ xx\ ((x^c)/(x^a))^b=1

    Text Solution

    |

  18. Prove that: 1/(1+x^(a-b))+1/(1+x^(b-a))=1

    Text Solution

    |

  19. Prove that: 1/(1+x^(b-a)+\ x^(c-a))+1/(1+x^(a-b)+\ x^(c-b))+1/(1+x^(b-...

    Text Solution

    |

  20. Prove that: (a+b+c)/(a^(-1)\ b^(-1)+b^(-1)\ c^(-1)+c^(-1)a^(-1))=abc

    Text Solution

    |