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

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- la consoleLv 71 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

- PinkgreenLv 71 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.

- fcas80Lv 71 month ago
As long as you use parentheses, it is + x^4. Without the parentheses, -x^4 is (-1)*(x^4)

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- ?Lv 71 month ago
(-x)⁴ = (-x) • (-x) • (-x) • (-x)

= [(-x) • (-x)] • [(-x) • (-x)]

= x² • x²

= x⁴

Note that in general, x⁴ ≠ x

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