📚 Topic Summary
The Power of a Power property is a rule in algebra that simplifies expressions where a power is raised to another power. In simpler terms, when you have an expression like $(a^m)^n$, the property states that you can multiply the exponents, resulting in $a^{m*n}$. This rule helps to condense and simplify complex exponential expressions, making them easier to work with in equations and calculations. It's a fundamental concept for manipulating exponents effectively.
This quiz will test your understanding of the Power of a Power property through vocabulary, fill-in-the-blanks, and critical thinking exercises. Good luck!
🧠 Part A: Vocabulary
Match each term with its correct definition. Write the corresponding number in the space provided.
| Term |
Definition |
| 1. Base |
a. The number of times the base is multiplied by itself |
| 2. Exponent |
b. An expression of the form $a^n$ |
| 3. Power |
c. The number that is being multiplied |
| 4. Power of a Power |
d. A rule stating $(a^m)^n = a^{m*n}$ |
| 5. Simplify |
e. To rewrite an expression in its most basic form |
Answers:
1. ___
2. ___
3. ___
4. ___
5. ___
✏️ Part B: Fill in the Blanks
Complete the following paragraph using the words provided: exponent, base, multiply, power, simplified.
The Power of a Power property helps simplify expressions. When raising a _____ to another _____, you _____ the exponents. For example, $(x^2)^3$ can be _____ to $x^6$. In this example, 'x' is the _____. This makes the expression easier to use.
🤔 Part C: Critical Thinking
Explain in your own words why the Power of a Power property works. Use an example to illustrate your explanation.