📚 Topic Summary
The 'power to a power' rule is a fundamental concept in algebra that simplifies expressions with exponents. It states that when you raise a power to another power, you multiply the exponents. In other words, $(a^m)^n = a^{m*n}$. This rule makes it easier to handle complex exponential expressions.
For instance, if we have $(2^3)^2$, we can simplify it as $2^{3*2} = 2^6 = 64$. Understanding this rule is crucial for solving equations and simplifying algebraic expressions involving exponents.
🧮 Part A: Vocabulary
Match the terms with their definitions:
- Term: Exponent
- Term: Base
- Term: Power
- Term: Simplify
- Term: Variable
Definitions:
- A symbol that represents a number.
- The number that is multiplied by itself when raised to a power.
- The small number that indicates how many times the base is multiplied by itself.
- To reduce an expression to its simplest form.
- An expression of the form $a^b$, representing repeated multiplication.
✍️ Part B: Fill in the Blanks
Complete the following paragraph with the correct terms:
The power to a power rule states that when you raise a ______ to another ______, you ______ the ______. For example, $(x^2)^3$ becomes $x$ to the power of ______, which is $x^6$. This ______ simplifies ______ expressions.
🤔 Part C: Critical Thinking
Explain, in your own words, why the power to a power rule works. Provide an example to support your explanation.