how do you simplify this expression?

Question

2^-1
________
2^-2+2^-3

Answer 1

So you want to simplifer

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

The first thing you want to do is convert them all to positive powers. Note that this can be done by putting "one over" them.

(1/2^1) / [ 1/2^2 + 1/2^3 ]

Now, what you want to do is multiply the top and bottom by the lowest common denominator. In this case, it's 2^3.

[(1/2^1) * (2^3)] / [ [1/2^2 + 1/2^3] * 2^3 ]

Note that the purpose of doing this is to eliminate ALL fractions within fraction, and that's what just happens. All of the denominators cancel out, but they leave you with stuff.

[2^2] / [2^1 + 1]

Then, you solve as normal.
4 / 3

Answer 2

Negative exponents mean reciprocals so 2^-1 = 1/2,
2^-2 = 1/4 and 2^-3 = 1/8

1/4 + 1/8 = 3/8 so you have (1/2)/(3/8)

which is 1/2 times 8/3 = 8/6 or 4/3