which expression is equivalent to (x^1/4 y ^16)^1/2

Question

which expression is equivalent to (x^1/4 y ^16)^1/2

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    0
    2021-10-04T16:15:38+00:00

    Answer:

    x^{\frac{1}{8}}y^{8}

    Step-by-step explanation:

    Consider the given expression

    (x^{\frac{1}{4}}y^{16})^{\frac{1}{2}}

    According to the distributive property of exponent,

    (ab)^m=a^mb^m

    Using distributive property of exponent we get

    (x^{\frac{1}{4}})^{\frac{1}{2}}(y^{16})^{\frac{1}{2}}

    Using the property of exponent we get

    x^{\frac{1}{4}\times \frac{1}{2}}y^{16\times \frac{1}{2}}           [\because (a^m)^n=a^{mn}]

    x^{\frac{1}{8}}y^{8}

    Therefore, the expression x^{\frac{1}{8}}y^{8} is equivalent to the given expression.

    0
    2021-10-04T16:16:02+00:00

    Answer:

    Equivalent expression is x^{\frac{1}{8}}y^{8}

    Step-by-step explanation:

    Given Expression is

    (x^{\frac{1}{4}}y^{16})^{\frac{1}{2}}

    We have to find Equivalent expression to given expression.

    using law of exponent , (ab)^x=a^xb^x

    we get,

    \implies(x^{\frac{1}{4}})^{\frac{1}{2}}(y^{16})^{\frac{1}{2}}

    now using another law of exponent, (x^a)^b=x^{ab}

    we get,

    \implies x^{\frac{1}{4}\times\frac{1}{2}}y^{16\times\frac{1}{2}}

    \implies x^{\frac{1}{8}}y^{8}

    Therefore, Equivalent expression is x^{\frac{1}{8}}y^{8}

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