Trigonometry Help Please?

Which of the following expressions are equivalent to x^4/7? why?

(x^4)^1/7 (4th rootx)^7 (7throotx)^4

(x^1/7)^4 4th rootx^7 7th rootx^4

1 Answer

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  • Anonymous
    1 decade ago
    Favorite Answer

    General Rules of Indices include:

    a^(p / q) is equivalent to the q-th root of x^p.

    a^(- p / q) is equivalent to 1 / [ a^(p / q) ].

    (a^p)^q = a^(pq).

    (x^4)^(1 / 7) = x^(4 * 1 / 7) = x^(4 / 7)

    [ x^(1 / 7) ]^4 = x^(4 * 1 / 7) = x^(4 / 7)

    (4th root of x)^7 = [ x^(1 / 4) ]^7 = x^(7 / 4)

    4th root of (x^7) = (x^7)^(1 / 4) = x^(7 / 4)

    (7th root of x)^4 = x^(4 / 7)

    7th root of (x^4) = x^(4 / 7).

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