Question

Which of these is equal to 4 (−)4
A.()4 B.(−)4 .−()4 D. (−)4

Answer 1

(a)
`x^4 * (-y)^4 = (xy)^4`

Explanation:

Given

`x^4 * (-y)^4`

Required

Select and equivalent expression

`A.\ (xy)^4`
`B.\ (-xy)^4`
`C.\ -(xy)^4`
`D.\ (x-y)^4`

`x^4 * (-y)^4`

Apply law of indices:

`x^4 * (-y)^4 =x^4 * (-y) * (-y) * (-y) * (-y)`

This gives:

`x^4 * (-y)^4 = x^4 * (y) * (y) * (y) * (y)`

`x^4 * (-y)^4 =x^4 * y^4`

x and y have the same exponent; So, they can be expressed as:

`x^4 * (-y)^4 = (x*y)^4`

`x^4 * (-y)^4 = (xy)^4`