# Power and Exponential Functions

### Instructions

- The first videos below explain the concepts in this section.
- This page also includes exercises that you should attempt to solve yourself. You can check your answers and watch the videos explaining how to solve the exercises.

### Concepts

- Properties of exponents applied to power and exponential expressions
- Multiplying and simplifying power expressions and exponential expressions
- Nested exponents and distributing exponents across multiplication and division
- Simplifying expressions with power and exponential functions

### Exercises

**Directions:**You should attempt to solve the problems first and then watch the video to see the solution.

- Simplify the following expressions.
- \(\dfrac{6x^2y^3}{18x^6y^4}\)
- \(\dfrac{2^x\cdot3^4}{2^8\cdot 3^y}\)

- Simplify the following expressions.
- \(\left(\dfrac{2x^3y}{y^2z^2}\right)^4\)
- \(\left( \dfrac{49\cdot 4^{-x}}{64\cdot 7^y}\right)^3\)

- Simplify the following expression. \[\left( \dfrac{2x^{-2}z^5}{3x^4y^{-11}}\right)^{-2}\]

- Simplify the following expression.\[\left( \dfrac{2^xy^3z^5}{24y^7z^{-1}}\right)^{-4}\]