Does -4^-4 simplify to a negative number?

Question

whpalmer4 · Answer

Let's clarify something: is that supposed to be 

$$(-4)^{-4}$$or$$-(4^{-4})$$
?

anonymous · Answer

If its the top one then yes. If its the bottom one then no.

whpalmer4 · Answer

@jsz I'll give you a medal if you explain why so @JerryK can learn something from this...

anonymous · Answer

It's top!

anonymous · Answer

I'm sorry. The bottom one will simplify to a negative number. -(2)^2=-4 because the negative sign is outside the parentheses. If it were inside the parentheses(-2)^2 =4. It is like multiply by -1 after you square the number. Also remember -2^-4 is like -1/2^4. A negative exponent is a simply a fraction.

anonymous · Answer

if its the top it will simplify to a positive number.

whpalmer4 · Answer

Yep!

If $a\ne0$, $a^{-n} = \dfrac{1}{a^n}$  That means our problem can be rewritten as $$(-4)^{-4} = \frac{1}{(-4)^4}$$And because an negative number raised to an even power becomes a positive number, that gives us the answer: a positive number.

anonymous · Answer

Nice Work. What math are you taking?

whpalmer4 · Answer

I think the last time I took a math class, I was less than half my current age, and it was in the 20th century :-)

anonymous · Answer

Lol