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Math Help - Rational Exponents

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    Rational Exponents

    I don't understand this.
    <br />
x^3/2-x^1/2 = 0

    For the problem, you're suppose to factor out a 1/2. I don't get that. You can't just go ahead and subtract?

    Someone please explain this problem to me.

    x^3/2=x^1/2

    ...3/2 and 1/2 are the exponents.
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    Member SENTINEL4's Avatar
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    x^\frac{3}{2}=x^\frac{1}{2} is your problem?
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    yes it is
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    Member SENTINEL4's Avatar
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    x^\frac{3}{2}-x^\frac{1}{2}=0 \Rightarrow x^\frac{1}{2}(x-1)=0
    So the solutions are x=0 or x=1
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    Quote Originally Posted by A Beautiful Mind View Post
    yes it is
    You can only subtract when the powers divide. If you had x^{\frac{3}{2}} \div x^{\frac{1}{2}} then you could subtract the exponents.

    You can also think of it as the definition of exponents:

    a^3 -a^2 = a \times a \times a - a \times a \neq a^{3-2}

    By inspection it would appear only 0 and 1 are solutions and this can be confirmed by factorising:

    x^{\frac{3}{2}} - x^{\frac{1}{2}} = x^{\frac{1}{2}}(x-1)= 0

    Either \sqrt{x} = 0 \: \rightarrow \: x = 0 \: \text { or }\: (x-1) = 0 \: \rightarrow \: x = 1
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    Quote Originally Posted by A Beautiful Mind View Post
    I don't understand this.
    <br />
x^3/2-x^1/2 = 0

    For the problem, you're suppose to factor out a 1/2. I don't get that. You can't just go ahead and subtract?

    Someone please explain this problem to me.

    x^3/2=x^1/2

    ...3/2 and 1/2 are the exponents.
    Well, just factoring isn't going to help you (well it will in this case, because its a pretty obvious question).

    You want to first arrange your terms, and then solve the resultant equation:

    [X^(3/2)]-[X^(1/2)]=0

    Factoring out an X^(1/2) and not just a (1/2) yields:

    [X^(1/2)][X^(2/2)-1], which is of course just (X-1). From there it should be fairly easy to figure out what you're answers are.
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