math problem?

How would you solve by (reducing, simplifying and rationalizing) the following problem?

the 4th root of 10a^5b^3/20ab^6?

Comments

  • 4th root(10a^5 b^3/ 20 ab^6)

    = 4th root(a^4/2b^3)

    =4th root(a^4/2b^3) x 4th root(8b/8b)

    =4th root(8a^4 b/16b^4)

    = 4th root(8b) x 4th root(a^4 /16b^4)

    =a 4th root(8b)/2b

  • The first thing to do is to recognise that division symbol in the middle of the equation.

    Then simplify; Fourth root of 10 (a*5b*3) / 20 (ab*6)

    10 (a*5b*3) multiplied by

    (1 / 20) ( a*-1b*-6) Note the negative integers. What have I done? What does a negative integer mean. You check it out.

    Simplify further: (10 / 20)( a* (5-1)b*(3-6))

    1/2 (a*4b*-3)

    Rationalise: 1 (a*4) / 2 (b*3)

    Fourth root of a to the power of 4 is simply a, so:

    a / fourth root [2b*3]

    And at that point I am stuck. But I hope this gets you on your way. Now refer to your text book to move on. I don't have a text any longer, so cannot refer.

    Now, wasn't that an interesting assignment? Can you see how it is designed not only to flush the goats from the sheep,

    or vice versa, but to give your mind a real tug into the "I'm not going to let it beat me" stakes?

    I just know you will enjoy finishing it off. Don't you just wish they would add an integer capacity into these keyboards so it could be done properly and visibly? It was already incorporated into scientific typewriter keyboards 37 years ago. Nobody had computers then but gigantic corporations.

    did you know there is more computing capicity in your desktop to-day than accompanied the lunar landing operations 39 years ago? Amazing, isn't it?

  • 10/20 * a^5/a * b^3/b^6

    10/20 divide both by 10

    1/2

    a^5 and a greatest common factor is a.

    a^4/1

    b^3/b^6= 1/b^3

    1*a^4*1/2*1*b^3

    a^4/2b^3

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