Get Ready to Ace the Exponents Test!

We have had a successful cycle covering the fundamental rules of exponents. With the test coming up tomorrow, now is the time to consolidate your knowledge. This guide will review the key properties you need to know and how to apply them to both numerical problems and algebraic expressions with variables.

Key Concepts and Vocabulary

Based on our class notes (Lesson 6.1), you should be comfortable with the following properties where $a$ and $b$ are real numbers, and $m$ and $n$ are integers:

  • Product of Powers Property: When multiplying bases that are the same, add the exponents. $$a^m \cdot a^n = a^{m+n}$$
  • Quotient of Powers Property: When dividing bases that are the same, subtract the exponents. $$\frac{a^m}{a^n} = a^{m-n} \quad (a \neq 0)$$
  • Power of a Power Property: When raising a power to another power, multiply the exponents. $$(a^m)^n = a^{m \cdot n}$$
  • Power of a Product Property: Distribute the exponent to each factor inside the parenthesis. $$(ab)^m = a^m b^m$$
  • Negative Exponent Property: A negative exponent indicates the reciprocal. $$a^{-m} = \frac{1}{a^m} \quad (a \neq 0)$$
  • Zero Exponent Property: Any nonzero number raised to the power of zero is one. $$a^0 = 1 \quad (a \neq 0)$$

Scientific Notation: Don't forget our work on scientific notation! Remember that a number is in scientific notation if it is in the form $c \times 10^n$, where $1 \leq c < 10$ and $n$ is an integer.

Study Strategy

I strongly suggest going back and reviewing the video lessons from the past few days. To help you prepare, I have compiled several worksheets. Mastering these problems is the best indicator that you are ready for the test.

Practice Resources:

Final Thoughts

If you can complete the problems on these worksheets comfortably, you will do great on the test. Remember: you have to try the problem first! If you have attempted a problem and are still stuck, please reach out with your questions, and I will be happy to help clarify the solution.

Good luck studying!