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Math Help - fractional exponents - without calculators

  1. #1
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    fractional exponents - without calculators

    How does

    2/3 * (2)^3/2 = 4/3 * root 2

    i got as far as: 2/3 * root 2 ^ 3 but i cant seem to simplify.
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  2. #2
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    Quote Originally Posted by calculus0 View Post
    How does

    2/3 * (2)^3/2 = 4/3 * root 2

    i got as far as: 2/3 * root 2 ^ 3 but i cant seem to simplify.
    well...

    Are you familiar with this rule: x^a\times x^b = x^{a+b}?

    And the fact that x^{1/2}= \sqrt{x}?

    \frac{2}{3} \times 2^{3/2} = \frac{2}{3}\times2^1 \times 2^{1/2} = \frac{4}{3} \sqrt{2}.
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  3. #3
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    Quote Originally Posted by calculus0 View Post
    2/3 * (2)^3/2 = 4/3 * root 2
    Your equation is "wrong" due to poor bracketing; should be:
    2/3 * 2^(3/2) = 4/3 * root 2

    (2)^3/2 = 8/2 = 4 : kapish?
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  4. #4
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    Thank you anonymous!
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  5. #5
    Super Member Anonymous1's Avatar
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    Quote Originally Posted by Wilmer View Post
    Your equation is "wrong" due to poor bracketing; should be:
    2/3 * 2^(3/2) = 4/3 * root 2

    (2)^3/2 = 8/2 = 4 : kapish?
    Its just ambiguous, not wrong. For instance, MATLAB evaluates 2^3/2 as 2^{3/2}.

    So, MATLAB says your wrong.
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  6. #6
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    Quote Originally Posted by Anonymous1 View Post
    Its just ambiguous, not wrong. For instance, MATLAB evaluates 2^3/2 as 2^{3/2}.
    So, MATLAB says your wrong.
    MATLAB can say anything it wants, I care not;
    BUT 2^3/2 = 8/2 = 4

    The standard order of operations.
    The standard order of operations, or precedence, is expressed in the following chart.
    exponents and roots
    multiplication and division
    addition and subtraction
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