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Math Help - Create expressions

  1. #1
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    Create expressions

    Hi guys,

    the task:
    Create four expressions that, when simplified using the exponent laws, are equal to 4x^6
    Each expression should use at least one different exponent law. State which law(s) must be used to simplify each expression.

    Could somebody help me with that task and explain how to start creating expressions? Thanks.
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  2. #2
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    Re: Create expressions

    For example, 4x^2\cdot x^4 = 4x^6. You use the fact that x^a\cdot x^b=x^{a+b}.
    Thanks from ford2008
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  3. #3
    Member kalyanram's Avatar
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    Re: Create expressions

    All the previous examples posted by you has demonstrated addition,subtraction,multiplication and division of exponents. Create example based on these facts and post your attempt.

    Kalyan.
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  4. #4
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    Re: Create expressions

    Kalyan could you do me a favour and check my post "Trigonometry Word Wheel". I would really appreciate it to hear your opinion.
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  5. #5
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    Re: Create expressions

    So my expressions=

    1. Product Law = (4x^2) (x^4) = 4x^6

    2. Quotient Law = 4x^8
    ------
    4x^2

    = 4x^6

    3. Power of a Power Law = (4x^3)^2 = 4x^6

    4. Power of a Product Law = (4x^2) (x^4) = 4x^6

    Is that right?
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  6. #6
    Member kalyanram's Avatar
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    Re: Create expressions

    1. and 4. are the same. The only missing expression is \sqrt{16x^{12}} = 4x^6. This in fact similar operation as 2. with the only exception that you are taking a fraction exponent.

    Kalyan.
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  7. #7
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    Re: Create expressions

    What Law is it then? The missing expression?
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  8. #8
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    Re: Create expressions

    Quote Originally Posted by ford2008 View Post
    2. Quotient Law = 4x^8
    ------
    4x^2

    = 4x^6

    3. Power of a Power Law = (4x^3)^2 = 4x^6
    The coefficients (the numbers before x) in 2 and 3 are wrong.
    Thanks from ford2008
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  9. #9
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    Re: Create expressions

    Thank you emakarov,

    so it should be in 2 =

    16x^8
    ------
    4x^2

    and in 3 =

    (16x^3)^2

    Is that right? Do you know witch missing expression law kalyanram is meaning with his answer?
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  10. #10
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    Re: Create expressions

    #3 should be (2x^3)^2=4x^6
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  11. #11
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    Re: Create expressions

    Quote Originally Posted by ford2008 View Post
    Do you know witch missing expression law kalyanram is meaning with his answer?
    \sqrt[a]{x^b}=x^{b/a}.
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