1. Multiplication properties of Exponents
7-1 Notes for Algebra 1
Multiplication properties of Exponents

2. 7.1 pg o, 69-84(x3)

3. Monomial (only one term)
A number, a variable, or the product of a number and one or more variables with nonnegative integer exponents. An expression that involves division by a variable is not a monomial.

4. Constant
A monomial that is a real number.

5. Example 1: Identify Monomials
Determine whether each expression is a monomial. Write yes or no. Explain your reasoning. 1.) 17−𝑐 2.) 8 𝑓 2 𝑔 3.) ) 5 𝑡

6. Example 1: Identify Monomials
Determine whether each expression is a monomial. Write yes or no. Explain your reasoning. 1.) 17−𝑐 No, it involves subtraction, so it has more than one term. 2.) 8 𝑓 2 𝑔 Yes, it involves the product of a number and two variables. 3.) 3 4 Yes, the expression is a constant. 4.) 5 𝑡 No, it has a variable in the denominator.

7. Product of Powers 𝑥 3 ∙ 𝑥 6 𝑥 3+6 𝑥 9
To multiply two powers that have the same base, add their exponents.
𝑥 3 ∙ 𝑥 6
𝑥 3+6
𝑥 9

8. Example 2: Product of Powers
Simplify each expression. 1.) 𝑟 4 −12𝑟 7 2.) 6𝑐 𝑑 5 5 𝑐 5 𝑑 2

9. Example 2: Product of Powers
Simplify each expression. 1.) 𝑟 4 −12𝑟 7 2.) 6𝑐 𝑑 5 5 𝑐 5 𝑑 2 −12 𝑟 𝑐 6 𝑑 7

10. Power of a Power
To find the power of a power, multiply the exponents.
𝑥 3 6
𝑥 3∙6
𝑥 18

11. Example 3: Power of a Power
Simplify

12. Example 3: Power of a Power
Simplify

13. Power of a Product 2 𝑥 2 𝑦 5 𝑧 4 3 2 3 ∙ 𝑥 2∙3 ∙ 𝑦 5∙3 ∙ 𝑧 4∙3
To find the power of a product, find the power of each factor and multiply.
2 𝑥 2 𝑦 5 𝑧 4 3
2 3 ∙ 𝑥 2∙3 ∙ 𝑦 5∙3 ∙ 𝑧 4∙3
8𝑥 6 𝑦 15 𝑧 12

14. Example 4: Power of a Product
Express the volume of a cube with side length 5𝑥𝑦𝑧 as a monomial.

15. Example 4: Power of a Product
Express the volume of a cube with side length 5𝑥𝑦𝑧 as a monomial.
125𝑥 3 𝑦 3 𝑧 3

16. Simplify Expressions
To simplify a monomial expression, write an equivalent expression in which:
Each variables base appears exactly once,
There are no powers of powers, and
All fractions are in simplest form.

17. Example 5: Simplify Expressions

18. Example 5: Simplify Expressions