Mathematics

Question

Simplify the cubed root of six over the fourth root of six

six raised to the one twelfth power
six raised to the one fourth power
six raised to the four thirds power
six raised to the seven twelfths power

2 Answer

  • Answer:

    six raised to the one twelfth power

    Step-by-step explanation:

    The cubed root of 6/the fourth root of 6 equals (6^1/3)/(6^1/4)

    6^((1/3)-(1/4))

    6^((4-3)/12)

    6^1/12

  • The simplified form of the expression is six raised to the one twelfth power

    Given the expression

    • [tex]\dfrac{\sqrt[3]{6} }{\sqrt[4]{6} }[/tex]

    According to indices, this expression can also be written as:

    • [tex]\dfrac{(6)^{1/3}}{6^{1/4}}[/tex]

    Using the law of indices;

    [tex]\dfrac{a^m}{a^n} = a^{m-n}[/tex]

    Applying this expression will give:

    [tex]=\dfrac{6^{1/3}}{6^{1/4}} \\= 6^{1/3-1/4}\\=6^{4-3/12}\\=6^{1/12}[/tex]

    Hence the simplified form of the expression is six raised to the one twelfth power

    Learn more on indices here: https://brainly.com/question/8952483

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