Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

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

Relevance
• 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

• ?
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