3.1 Using Exponents to Describe Numbers

Transcription

1 .1 Using to Describe Numbers Represent repeated multiplication with exponents Describe how powers represent repeated multiplication Demonstrate the difference between the exponent and the base by building models of a given power, such as and. Demonstrate the difference between two given powers in which the exponent and the base are interchanged by using repeated multiplication, such as and. Evaluate powers with integral bases (excluding base 0) and whole number exponents., and Explain the role of parentheses in powers by evaluating a given set of powers such as Terminology : An expression made up of a base and an exponent Base: The number you multiply by itself in a power Exponent: The number of times you multiply the base in a power Exponential Form: A shorter way to write a repeated multiplication Example 1: Complete the chart Word Form Repeated Multiplication Exponential Form Evaluate Four cubed ( 1) Fifth power of Ten to the exponent four ( ) ( ) Example : Use a model to represent each of the following powers then evaluate. a) b) c) 5 d) 1 e) 1 Example : Are ( ) and equal? Investigate: What is the difference between and? (Hint: repeated multiplication vs repeated addition) Evaluate : Write each question as repeated multiplication then evaluate. a) ( ) b) c) ( ) d) ( 1) e) ( 5) f) 5 Riverside Secondary (created by Mrs. Wong) Page 1

2 g) h) i) 10 7 j) ( ) k) ( ) l) ( ) m) ( 5) n) ( ) Show you know: Do you think ( ) will be positive or negative? Why? Show you know: How does the multiplication rule for negative numbers apply to powers with negative bases?. Exponent Laws Explain the exponent laws for multiplying and dividing powers with the same base. Explain the exponent laws for raising a product and quotient to an exponent. Explain the law for powers with an exponent of zero. Use patterns to show that a power with an exponent of zero is equal to one. I can apply the laws of exponents. I can identify the error in a simplification of an expression involving powers. Example 1: Write each product of powers as repeated multiplication, then as a single power & evaluate. Product Repeated Multiplication Single Evaluate ( ) ( ) 5 Show you Know: Write a rule for Multiplying s of the SAME base. (Product Law) -When multiplying powers of the same base: Riverside Secondary (created by Mrs. Wong) Page

3 Example : Express the division of powers as repeated multiplication, reduce, write as a single power & evaluate. Quotient Repeated Multiplication Single Evaluate ( ) ( ) ( ) ( ) ( 1) ( 1) 5 5 Show you Know: Write a rule for Dividing s of the SAME base. (Quotient Law) -When dividing powers of the same base: Example : Express the power of a power as repeated multiplication, then write as a single power & evaluate. of a Repeated Multiplication Single Evaluate ( 10 ) ( 5 ) ( ) 1 ( ) 5 Riverside Secondary (created by Mrs. Wong) Page

4 Show you Know: Write a rule for raising a power to an exponent. ( Law) -When raising a power to an exponent: Practice: Write as a single power (if possible) then evaluate. 11 1) ( )( ) ) _ ) 1 ) 5 5) (5 ) _ ) 9 7) (0.1) ( 0.1 ) 7 8) ( ) ( ) ( ) 9) ( ) 8 Example : Express the division of powers as repeated multiplication & evaluate. Then write as a single power using the Quotient Rule. Quotient Repeated Multiplication Evaluate Single 7 7 ( ) ( ) ( ) ( ) Show you Know: Write a rule for a s with an Exponent of Zero. (Zero Law) Practice: Evaluate. 1 a. b. ( ) 0 c. 5 d. Riverside Secondary (created by Mrs. Wong) Page

5 More Practice: Write as a single power then evaluate. 1) ( ) ) 5 ( ) 5( ) ) 5 7 ) ( 1) 7( 1) 5) ) ( ) 15. Order of Operations Use the order of operations on expressions with powers. Determine the sum and difference of two powers. Identify the error in applying the order of operations in an incorrect solution. Follow the Order of Operations (BEDMAS) when evaluating expressions involving powers Brackets Divide & Multiply in order from left to right Add & Subtract in order from left to right Example 1: Evaluate a) ( ) b) ( ) c) 8 + ( ) d) 8 + ( ) e) ( 15 ) ( ) + + f) + Riverside Secondary (created by Mrs. Wong) Page 5

6 . Using to Solve Problems Use powers to solve problems. Solve problems by applying the order of operations. Example 1: Write an expression involving powers to represent the Shaded Area of the following overlapping squares with each given side length, then evaluate: a) b) c) cm cm 1cm 5cm cm cm cm d) e) cm f) 1 cm cm 1cm 1 cm cm Example : What is the volume & surface area of a cube with an edge length of 5 m? 5m Example : What is the volume & surface area of a cube with an edge length of m? Example : How much larger is the volume of the cube with a side length of 5 m compared to the cube with side length of m? Riverside Secondary (created by Mrs. Wong) Page

7 Example 5: Write as a power the volume of the shaded space of the following cubes with each given side length, then evaluate: a) b) cm cm cm cm Example : Find the side length of the shaded square attached to the right triangle with the given side lengths in the diagrams: a) b) m m 1m 5m Example 7: A circle is inscribed in a square with a side length of 10 cm. What is the area of the shaded region? 10cm Example 8: A colony of bacteria triples every hour. There are 100 bacteria now. How many will there be after each amount of time? Show your work. a) 1 hour b) hours c) 1 hours d) n hours Riverside Secondary (created by Mrs. Wong) Page 7