Please help with this math Problems? Negative Exponents?

Question

pls help there are other similar ones...so if you can explain these ill be able to do the rest. thanks!!!

1) 3-(-1)^4

2) - (2^7)(2^ -3)

3) (1/3)^-1 + (1/2) ^ -1

Answer 1

1)
First raise -1 to the fourth power:
(-1)^4 = [(-1)²]² = [(-1)*(-1)]² = (1)² = 1
3 - 1 = 2

2)
First raise 2 to the seventh power, then multiply that by -1:
(2)^7 = 128
-[(2)^7] = -128
Now raise 2 to the negative third power:
(2)^-1 = 1/2.
So (2)^-3 = [(2)^-1]^3 = (1/2)^3 = 1/[(2)^3] = 1/8.
This problem then becomes (-128)(1/8) = -16

3)
(1/3)^-1 = 1/[(3)^-1] = 1/(1/3) = 3
By similar reasoning, (1/2)^-1 = 1/[(2)^-2] = 1/(1/2) = 2
So this problem becomes 3 ÷ 2 = 1 + ½ or 1.5