Question

Question #e4bbb

Answer 1

Break down the power.

Explanation:

Essentially, break down the power into two separate powers, 1/4 and whatever the other one is.
`2^4=16, therefore 2=16^(1/4)`

Going through each question:
1.
`16^(3/4)=(16^(1/4))^3=2^3=8`
2.
`16^(-3/4)=(16^(1/4))^-3=2^-3=1/8`
3.
`-16^(3/4)=-(16^(1/4))^3=-2^3=-8`
4. In case you know what imaginary numbers are, (If not, forget about question 4, it doesn't have a real answer):
`(-16)^(3/4)=((-16)^(1/4))^3=(2sqrti)^3=(2(1/sqrt2+1/sqrt2i)^3)`
Possibly remembering that powers of complex numbers multiply angles and yadda yadda:
`=8(sqrt2i-sqrt2)=8sqrt2i-8sqrt2`

Hope this helped. Like I said, if you don't know what is going on in question 4, just say it doesn't have a real answer because you can't take the square root of -1.