MATHEMATICS8 Q1 4. Base and Exponents.pptx

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1. Base and Exponents

2. Objectives: Write a product using exponents. Illustrate and prove the product rule for exponents. Illustrate and apply the first power rule for exponents. Illustrate, prove. and apply the quotient rule for exponents.

3. Exponent Notation Base Exponent Expanded Form Value Read as 7 2 7 x 7 49 Seven squared or seven to the power of two 2 3 2 x 2 x 2 8 Two cubed or two to the power of three Exponent Notation Base Exponent Expanded Form Value Read as 7 2 7 x 7 49 Seven squared or seven to the power of two 2 3 2 x 2 x 2 8 Two cubed or two to the power of three

4. To indicate repeated multiplication, we can use natural number exponents. Examples are:        

5. Natural Number Exponents If n is a natural number, then   Natural numbers are the counting numbers. When a number or variable is raised to a natural number exponent , it means repeated multiplication .

6. In the expression , x is called the base , and n is called the exponent . The whole expression is called the nth power of x.     Exponent Base

7. An exponent, which is a natural number, tells how many times its base is to be used as a factor. An exponent of 1 means that its base is to be used one time as a factor; an exponent of 2 means that its base is to be used two times as a factor; and so on. Thus, =   = -x   = (-3p) (-3p)   = 4  

8. Write each product using exponents. -(        

9. Product Rule for Exponents If m and n are natural numbers, then: =   In words, to multiply two exponential expressions with the same base, keep the base and add the exponents.

10. Simplify each Expression. x³ x⁴ =   2⁵ 2² =   a⁶ a³ =   m × m² =   y⁴ y⁵ y =  

11. Power Rule for Exponents If m and n are natural numbers, then: =   In words, to raise an exponential expression to a power, keep the base and multiply the exponents.

12. Simplify         Any base to the power of 0 is 1

13. Product-to-Power Rule for Exponents For any factors x and y and integer exponent n : ( =   In words, You distribute the exponent to each factor inside the parentheses.

14. Simplify        

15. Quotient Rule of exponents   (   In words, When you divide powers that have the same base , subtract the exponents .

16. Simplify      

17. Quotient-to-Power Rule for Exponents     In words, When a fraction (quotient) is raised to a power, apply the exponent to both the numerator and the denominator .

18. Simplify and express your answers in exponential form.        

19. Quiz

20. Simplify the following expressions. Copy and answer. Show your complete solution. ✏ Note: Erasures mean wrong. 2. a⁵ a² 3. 4. 5.  

21. Simplify the following expressions. Copy and answer. Show your complete solution. ✏ Note: Erasures mean wrong. 7. 8. 9. 10. (3² 3²)²