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21 January, 00:53

Which expression is equivalent to [ (3xy^-5) ^3 / (x^-2y^2) ^-4]^-2

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  1. 21 January, 01:07
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    The answer is (x ¹⁰ y ¹⁴) / 729.

    Explanation:

    We can begin simplifying inside the innermost parentheses using the properties of exponents. The power of a power property says when you raise a power to a power, you multiply the exponents. This gives us

    [ (3 ³ x ³ y ⁻¹⁵) / (x ⁸ y ⁻⁸) ] ⁻².

    Negative exponents tell us to "flip" sides of the fraction, so within the parentheses we have

    [ (3 ³ x ³ y ⁸) / (x ⁸ y ¹⁵) ] ⁻².

    Using the quotient property, we subtract exponents when dividing powers, which gives us

    (3 ³ / x ⁵ y ⁷) ⁻².

    Evaluating 3 ³, we have

    (27/x ⁵ y ⁷) ⁻².

    Using the power of a power property again, we have

    27 ⁻² / x ⁻¹⁰ y ⁻¹⁴.

    Flipping the negative exponents again gives us x ¹⁰ y ¹⁴ / 729.
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