Powers of Powers

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1. Powers of Powers

   Lesson 1-1 — Numbers and Operations

2. Laws We Need

   Review single base before power of a power

3. Conditions for Zero and Negative Exponents

   Keep each law with its domain condition

4. Get Ready: Cube Aquarium

   From edge length to volume

5. Think and Discuss

   Different expressions, one algebraic value

6. Power of a Power Law

   Exponents are multiplied

7. Example 1 (1)

   Power of a power, then add and subtract exponents

8. Example 1 (2)

   Negative exponents and the original domain

9. Example 1 (3)

   Rewrite 4, 9, and 6 using bases 2 and 3

10. Power of a Product and Quotient

    Distribute the outer exponent to each factor

11. Example 2 (1)

    Distribute the outer exponent and track the sign

12. Example 2 (2)

    Power of a quotient with negative exponents

13. The Sign is Part of the Base

    Parentheses make a difference

14. Example 3: Simplify

    Factor 9, 18, and 36, then collect each prime base

15. Example 3: Substitute

    Find the numerical value when n = 2

16. Example 4: The Room and the Tile

    Divide the areas, not the side lengths