Section 5.1 Product and Power Rules for Exponents

5.1 Lecture Guide: Product and Power Rules for Exponents Objective: Use the product rule for exponents.

Exponential Notation Algebraically For any natural number n, with base b and exponent n. Verbally For any natural number n,is the product of b used as a factor n times. Numerical Examples The expressionis read as “b to the nth power.”

Write each exponential expression in expanded form. 1.

2. Write each exponential expression in expanded form.

3. Write each exponential expression in expanded form.

4. Write each exponential expression in expanded form.

Write each expression in exponential form. 5.

Write each expression in exponential form. 6.

Write each expression in exponential form. 7.

Write each expression in exponential form. 8.

9. Complete the warm-up examples below: Expanded Form: Shortcut:

Algebraic Examples For any real number x and natural numbers m and n, To multiply two factors with the same base, use the common base and ____________ the exponents. ____________ Product Rule for Exponents: Algebraically Verbally

Simplify each expression. 10.

11. Simplify each expression.

12. Simplify each expression.

13. Simplify each expression.

14. Expanded Form: Shortcut: Objective: Use the power rule for exponents. Complete the warm-up examples below:

Algebraic Examples For any real number x, and natural numbers m and n, To raise a power to a power, ____________ the exponents. ____________ Power Rule for Exponents: Verbally Algebraically

Simplify each expression. 15.

16. Simplify each expression.

17. Simplify each expression.

18. Simplify each expression.

19 Simplify each expression.

20. Expanded Form: Shortcut: Complete the warm-up examples below:

Algebraic Examples For any real number x and y and any natural number m, To raise a product to a power, raise each ____________ to this power. ____________ Raising Products and Quotients to a Power: Algebraically Verbally

Algebraic Examples For any real number x and y and any natural number m, To raise a quotient to a power, raise both the ____________ and the ____________ to this power. ____________ Raising Products and Quotients to a Power: Algebraically Verbally

Simplify each expression. 21.

22. Simplify each expression.

23. Simplify each expression.

24. Simplify each expression.

25. Simplify each expression.

26. Simplify each expression.

27. Simplify each expression.

28. Simplify each expression.

29. Evaluate the expression forand,,

Comparing Addition and Multiplication Add the like terms and simplify the products

Comparing Addition and Multiplication Add the like terms and simplify the products

Comparing Addition and Multiplication Add the like terms and simplify the products If possible, addIf possible, multiply

36. The formula for the area of a square is where x is the length of a side of the square. (a) Complete the table of values for the area of a square with sides of length x cm. Length of a side, x cm Area

36. The formula for the area of a square is where x is the length of a side of the square. (b) How does the area of a square with sides of length 2 cm compare to the area of a square with sides of length 4 cm? 2 cm 4 cm