Which property of exponents must be used first to solve this expression? (iy2)1/3

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Which property of exponents must be used first to solve this expression? (iy2)1/3

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Nho 5 years 2021-08-17T13:01:04+00:00 1 Answers 24 views 0

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  1. Ben
    0
    2021-08-17T13:02:17+00:00
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    Step-by-step explanation:

    “must be used first” is a very hard phrasing. multiplication is commutative.

    and I am not sure that the problem is stated correctly.

    I read here

    (i×y²) to the power of 1/3.

    i is the imaginary constant sqrt(-1) ?

    exponents brought themselves to the power of something else multiply.

    e.g.

    ({2}^{3})^{4} = {2}^{12}

    exponents in multimedia expressions of the same base simply add up.

    e.g.

    {2}^{3} \times {2}^{4} = {2}^{7}

    a negative exponent means that the expression with the same positive exponent is just at the bottom of a division.

    e.g.

    {2}^{ - 3} = 1 \div {2}^{3}

    and a fraction as exponent specifies a root to be taken.

    e.g

    {2}^{1 \div 3} = \sqrt[3]{2}

    so, I would do all the exponent multiplications to simplify the expression.

    \sqrt[3]{i \times {y}^{2} } = ({i \times {y}^{2} })^{1 \div 3} =

    = ( { - 1}^{1 \div 2} \times {y}^{2} ) ^{1 \div 3}

    1/2 × 1/3 = 1/6

    2 × 1/3 = 2/3

    = { - 1}^{1 \div 6} \times {y}^{2 \div 3} = \sqrt[6]{ - 1} \times \sqrt[3]{ {y}^{2} }

    so, as we can see, we can move freely from multiplying the fraction exponents to converting them into root expressions and vice versa.

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