Answer:
(a) [tex]x^4 * (-y)^4 = (xy)^4[/tex]
Step-by-step explanation:
Given
[tex]x^4 * (-y)^4[/tex]
Required
Select and equivalent expression
[tex]A.\ (xy)^4[/tex] [tex]B.\ (-xy)^4[/tex] [tex]C.\ -(xy)^4[/tex] [tex]D.\ (x-y)^4[/tex]
[tex]x^4 * (-y)^4[/tex]
Apply law of indices:
[tex]x^4 * (-y)^4 =x^4 * (-y) * (-y) * (-y) * (-y)[/tex]
This gives:
[tex]x^4 * (-y)^4 = x^4 * (y) * (y) * (y) * (y)[/tex]
[tex]x^4 * (-y)^4 =x^4 * y^4[/tex]
x and y have the same exponent; So, they can be expressed as:
[tex]x^4 * (-y)^4 = (x*y)^4[/tex]
[tex]x^4 * (-y)^4 = (xy)^4[/tex]
