Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Why does (-x)^4 = x^4 not (-x)^4 = x?

6 Answers

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  • 1 month ago

    = (- x)^(4)

    = (- x) * (- x) * (- x) * (- x)

    = [(- x) * (- x)] * [(- x) * (- x)] → the product of two numbers with the same sign is positive

    = [+ x²] * [+ x²] → the product of two numbers with the same sign is positive

    = + x⁴

    = x⁴

  • 1 month ago

    (-x)^4=x^4

    =>

    x^4=x^4

    =>

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

    =>

    x=x

    =>

    x can be any number & the given is an identity.

    But

    (-x)^4=x

    =>

    x^4=x

    =>

    x^3=1 (if x=/=0)

    =>

    x^3-1=0

    =>

    (x-1)(x^2+x+1)=0

    =>

    x=1

    or

    x=[-1+/-sqr(3)i]/2

    =>

    the given is not an identity.

    Thus, the 2 given are not the same.

  • fcas80
    Lv 7
    1 month ago

    As long as you use parentheses, it is + x^4.  Without the parentheses, -x^4 is (-1)*(x^4)

  • 1 month ago

    (-x)^4 = x^4

    x^4 = x^4

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  • ?
    Lv 7
    1 month ago

    (-x)⁴ = (-x) • (-x) • (-x) • (-x)

           = [(-x) • (-x)] • [(-x) • (-x)]

           =  x² •  x²

           = x⁴

    Note that in general, x⁴ ≠ x

  • ted s
    Lv 7
    1 month ago

    ( - x )(-x)(-x)(-x) ╪ x

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