(4(a^-2)(b^3))^-3 = (4^(-3)) (a^(-2-3)) (b^(3-3)) = (1/(4^3))(a^(-5))(b^0) = (1/64)(a^(-5))(1) = 1/(64a^5).

2. Easiest here is to notice that 36 = 6^2. When you take powers, the exponents multiply, so:

36^(3/2) = (6^2)^(3/2) = 6^(2(3/2)) = 6^3 = 216.

Write it out the normal way, without ^, to see what’s going on.

3. Same type of problem as previous one.

32^(-3/5) = (2^5)^(-3/5) = 1/8. (You do the intermediate steps)

4. Here you have to know the standard formula (a^3 – b^3) = (a – b)(a^2 + ab + b^2).

(x^3) – 8 = (x^3) – (2^3) = (x – 2)(x^2 + 2x + 4).

5. Same as previous, formula here is (a^3 + b^3) = (a + b)(a^2 – ab + b^2).

125 + (n^3) = (5^3) + (n^3) = you work it out.

In many of these problems on powers, the key is to check whether the NUMBERS used are simple powers. Write out the first few powers of the numbers from 2 to 10 so you will recognize them easily.