1. ALGEBRA READINESS LESSON 10-1 Warm Up Lesson 10-1 Warm-Up

2. ALGEBRA READINESS LESSON 10-1 Warm Up Lesson 10-1 Warm-Up

3. ALGEBRA READINESS “Properties of Exponents” (10-1) How do you multiply numbers with the same base? How do you multiply powers in algebraic expressions? Rule: When you multiply exponents with the same nonzero base (a ≠ 0), add the exponents. Example: 2 3 + 2 4 = (2 · 2 · 2) + (2 · 2 · 2 · 2) = 2 3+4 = 2 7 Example: -2x · 3x 5 = -2 · 3 · x 1 · x 5 = -6 · x 1+5 -6x 6 To multiply power in algebraic expressions, multiply the coefficients together and add the exponents of like terms (same variables) together. Example: a m · a n = a m+n

4. ALGEBRA READINESS a.) Write the expression using a single exponent. (–3) 2 (–3) 4 = (–3) 6 Simplify the exponent. Add the exponents. = (–3) 2+4 (–3) 4 (–3) 2 Properties of Exponents LESSON 10-1 Additional Examples

5. ALGEBRA READINESS “Properties of Exponents” (10-1) How do you divide powers with the same base? Rule: When you divide numbers with the same base, subtract the exponents. Example: = a 2 a m = a m - n a n a 4 = a · a · a · a a 2 = a · a 1 1 1 1

6. ALGEBRA READINESS b.) Simplify each expression. x4x9x4x9 a. Simplify the exponents.= x –5 Rewrite using positive exponents. 1x5 1x5 = p 3 j –4 p –3 j 6 = p 6 j –10 Simplify. Rewrite using positive exponents. p 6 j 10 = b. = Subtract exponents when dividing powers with the same base. x 4 – 9 = Subtract exponents when dividing powers with the same base. p 3 – (–3) j –4 – 6 Properties of Exponents LESSON 10-1 Additional Examples

7. ALGEBRA READINESS a.) Rewrite each expression using each base only once. 7 3 7 2 = 7 5 Simplify the sum of the exponents. 4 4 4 1 4 –2 = 4 3 Simplify the sum of the exponents. = 6 0 Simplify the sum of the exponents. Use the definition of zero as an exponent.= 1 a. b. 6 8 6 –8 c. Add exponents of powers with the same base. 7 3 + 2 = Think of 4 + 1 – 2 as 4 + 1 + (–2) to add the exponents. 4 4 + 1 – 2 = Add exponents of powers with the same base. 6 8 + (–8) = Properties of Exponents LESSON 10-1 Additional Examples

8. ALGEBRA READINESS b.) Simplify each expression. p 2 p p 5 a. = p 8 Simplify. Multiply the coefficients. Write q as q 1. = 24(p 3 ) (q 1 q 4 ) Simplify. = 24p 3 q 5 2q 3p 3 4q 4 b. Commutative and Associative Properties of Multiplication (2 3 4)(p 3 )(q q 4 ) = Add exponents of powers with the same base. p 2 + 1 + 5 = Add exponents of powers with the same base. = 24(p 3 ) (q 1 + 4 ) Properties of Exponents LESSON 10-1 Additional Examples

9. ALGEBRA READINESS “Properties of Exponents” (10-1) How do you divide numbers in scientific notation form? Rule: When you divide numbers in scientific notation, divide the decimals and the exponents separately. Example: To find average, divide the number of tons by number of people

10. ALGEBRA READINESS c.) A small dog’s heart beats about 64 million beats in a year. If there are about 530 thousand minutes in a year, what is its average heart rate in beats per minute? 64 million beats 530 thousand min 6.4  10 7 beats 5.3  10 5 min =Write in scientific notation. 6.4 5.3  10 7–5 = Subtract exponents when dividing powers with the same base. 6.4 5.3  10 2 = Simplify the exponent. The dog’s average heart rate is about 121 beats per minute. Properties of Exponents LESSON 10-1 Additional Examples 121 Write in standard notation. 1.21  10 2 Divide. Round to the nearest hundredth.

11. ALGEBRA READINESS 1. Write (–8) 4 (–8) 5 using a single exponent. 2. Write using a single exponent. 3. Jupiter’s diameter is about 1.43 x 10 5 kilometers. Earth’s diameter is about 1.28 x 10 4 kilometers. How many times greater is Jupiter’s diameter than Earth’s diameter? Round the answer to the nearest tenth. 9393 (–8) 9 97949794 11.2 times greater Properties of Exponents LESSON 10-1 Lesson Quiz