How to calculate these algebra equations?

I'm assuming the * is indicating multiplication, not raising the value to a certain power.

When you multiply fractions, you literally just multiply across. That's it. Nothing fancy.

(4/1) * (2/3)

4 is the numerator in the first value and 2 is the numerator in the second value. Those two values multiplied together equal 8. 1 is the denominator in the first value and 3 is the denominator in the second value. Those two values multiplied together equal 3. Therefore, the answer to the problem is 8/3.

If the * is indicating raising the 4 to the value of (2/3), you must think of things in terms of radicals. sqroot2 is the same as 2^(1/2). That's just how things are. 4^(2/3) is therefore the same as (cuberoot4)^2.