Question

Which of the following simplifies to a negative number?

-4^-4
(-4)^-4
4^-4
1/4^-4

Answer 1

This is the correct answer people I just took the lesson. -4^-4

Answer 2

Option A is correct.

`-4^(-4)`

Explanation:

Using exponent rule:

`(a^(-n))^m =((1)/(a^n))^m = (1)/(a^(nm))`

Option A:

`-4^(-4)`

`-(4^(-1))^4 = -((1)/(4))^4 = -(1)/(4^4) = -(1)/(256)`

Option B:

`(-4)^(-4)`

`(-4)^(-4) = ((-4)^(-1))^(4) = ((1)/(-4))^4 = (1)/((-4)^4) = (1)/(256)`

Option C :

`4^(-4)`

`4^(-4) = (4^(-1))^4 = ((1)/(4))^4 = (1)/(4^4) = (1)/(256)`

Option D:

`((1)/(4))^(-4)`

`((1)/(4))^(-4) = (4^(-1))^(-4)=4^(4) = 256`

Therefore, the following simplifies to a negative number is,
`-4^(-4)`