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Thread: Simplify exponents with different bases

  1. #1
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    Simplify exponents with different bases

    x, y, and z are whole numbers and I have to simply this:


    x^(1/2) * y^(2/3) * z^(5/6)


    A) 3rd root of (x * y^2 * z^3)
    B) 6th root of (x * y^2 * z^5)
    C) 6th root of (x^3 * y^2 * z^5)
    D) 6th root of (x^3 * y^4 * z^5)
    E) 11th root of (x * y^2 * z^5)


    Well I tried getting:


    sqrt(x) * cuberoot(y^2) * sixthroot(z^5)


    Or something similar like:


    sqrt(x) * [cuberoot(y)]^2 * [sixthroot(z)]^5


    But not sure how to combine those terms.
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  2. #2
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    Re: Simplify exponents with different bases

    Quote Originally Posted by daigo View Post
    x, y, and z are whole numbers and I have to simply this:


    x^(1/2) * y^(2/3) * z^(5/6)


    A) 3rd root of (x * y^2 * z^3)
    B) 6th root of (x * y^2 * z^5)
    C) 6th root of (x^3 * y^2 * z^5)
    D) 6th root of (x^3 * y^4 * z^5)
    E) 11th root of (x * y^2 * z^5)
    rewrite all exponents with a common denominator
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  3. #3
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    Re: Simplify exponents with different bases

    Ah, I didn't know you were allowed to do that...would that be changing the value of the expression at all?
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  4. #4
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    Re: Simplify exponents with different bases

    Quote Originally Posted by daigo View Post
    Ah, I didn't know you were allowed to do that...would that be changing the value of the expression at all?
    no
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  5. #5
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    Re: Simplify exponents with different bases

    Skeeter is not suggesting that you replace only the denominators with the least common denominator, he is suggesting you replace each fraction with the corresponding equivalent fraction with that least common denominator.

    Surely you learned long ago that \frac{1}{2}= \frac{3}{6}. Because they are equal, using one rather than the other will not change the value of any formula: a^{1/2}= a^{3/6}
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