Question

Which of the following simplifies to a negative number?

Answer 1

Answer:

Option A is correct.

$-4^{-4}$

Step-by-step explanation:

Using exponent rule:

$(a^{-n})^m =(\frac{1}{a^n})^m = \frac{1}{a^{nm}}$

Option A:

$-4^{-4}$

$-(4^{-1})^4 = -(\frac{1}{4})^4 = -\frac{1}{4^4} = -\frac{1}{256}$

Option B:

$(-4)^{-4}$

$(-4)^{-4} = ((-4)^{-1})^{4} = (\frac{1}{-4})^4 = \frac{1}{(-4)^4} = \frac{1}{256}$

Option C :

$4^{-4}$

$4^{-4} = (4^{-1})^4 = (\frac{1}{4})^4 = \frac{1}{4^4} = \frac{1}{256}$

Option D:

$(\frac{1}{4})^{-4}$

$(\frac{1}{4})^{-4} = (4^{-1})^{-4}=4^{4} = 256$

Therefore, the following simplifies to a negative number is, $-4^{-4}$

Answer 2

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