I am really having problems with monomials: Please help!

Question

Simplify:

4x^2 y^3 Z
----------- (divided by)
5y^4 Z^3

is the answer
4x
------ (divided by)
5yz^2

Answer 1

With monomials, you can look at each unknown (variable) individually when you do a division:
4x²
------- = 4x²/5
5

y³/y⁴ = 1/y

z/z³ = 1/z²

So putting everything together:
4x^2 y^3 Z / 5y^4 Z^3
4x²/(5yz²)

Answer 2

Explain the difference in answers between the following exponential expressions. Include the solutions?

7^2, -7^2,(-7)^2, and 7^-2