Which of the following represents fourth root of x cubed in exponential form? x to the three fourths power x to the four thirds power 4x

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Which of the following represents fourth root of x cubed in exponential form? x to the three fourths power x to the four thirds power 4×3 3×4

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    2021-09-10T09:22:13+00:00

    Given: Fourth root of x cubed

    To Find: The corresponding mathematical expression

    Solution: The correct representation of the given statement is x to the three fourths power, i.e. x^{\frac{3}{4}}

    Explanation:

    The given statement is “fourth root of x cubed”. We will take the statement step wise to construct the correct expression.

    “Fourth root of x” corresponds to the expression \sqrt[4]{x}.

    This may also be written as x^{\frac{1}{4}}.

    Then, “fourth root of x cubed” means we have to cube the above ecpression, i.e., add the exponent 3.

    So we will have (x^{\frac{1}{4}})^3.

    Using the Rule of Exponents that for any integers a and b, (x^{\frac{1}{b}})^a= x^{\frac{a}{b}}, we can say

    (x^{\frac{1}{4}})^3=x^{\frac{3}{4}}

    So the correct representation of the given statement is x to the three fourths power.

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