Section 5.1 Product and Power Rules for Exponents

5.1 Lecture Guide: Product and Power Rules for Exponents Objective 1: Convert between exponential form and expanded form.

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 ____________ n times. The expression is read as “b to the nth power.” Numerical Example Exponential Notation

Write each expression in exponential form

Write each exponential expression in expanded form

Write each exponential expression in expanded form

Write each exponential expression in expanded form

11. Complete the warm-up examples below: Expanded Form: Alternate Form:

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

Simplify Each Expression

Simplify Each Expression

16. Expanded Form: Alternate form: Objective 3: Use the power rule for exponents. Complete the warm-up examples below:

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

Simplify Each Expression

Simplify Each Expression

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

Algebraically For any real numbers x and y and any natural number, m, Verbally To raise a product to a power, raise each ___________ to this power. To raise a quotient to a power, raise both the ________ and the _________ to this power. Algebraic Example _________________ Raising Products and Quotients to a Power

Simplify Each Expression

Simplify Each Expression

Simplify Each Expression

Simplify Each Expression

30. Evaluate the expression for and

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

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

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

37. 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, cm

37. The formula for the area of a square is (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 where x is the length of a side of the square.