1. ALGEBRA READINESS LESSON 5-7 Warm Up Lesson 5-7 Warm-Up

2. ALGEBRA READINESS LESSON 5-7 Warm Up Lesson 5-7 Warm-Up

3. ALGEBRA READINESS “Zero and Negative Exponents” (5-7) What if zero is an exponent? What if the exponent is a negative number? Rule: Zero as an Exponent: any nonzero (the base cannot be zero) number, a, with an exponent of zero equals 1. Examples: 5 0 = 1 (-2) 0 = 1 (1.02) 0 = 1 (½) 0 = 1 a 0 = 1 Proof: a 4 = a · a · a · a = 1 = 1 a 4 = a · a· a · a 1 So a 4-4 = a 0 = 1 Rule: Negative Exponent: A negative exponent means “the reciprocal of the base number”. In other words, put the base number under 1 to turn a negative exponent into a positive one. Example: Formality: Answers are Written With Only Positive Exponents: To eliminate a negative sign from an exponent, write the reciprocal of the base number. Example: Tip: When evaluating algebraic exponential expressions (algebraic expressions with exponents) for known values, write the expression with positive exponents before substituting known variables with their known values. a -3 = 1 a 3 1 = a 3 a -3 1 1 1 1 1 1 1 1 1

4. ALGEBRA READINESS Simplify (–4). = – 1 64 Simplify. –3 1 – 64 = Simplify the denominator. 1 (–4) 3 Use the rule for negative exponents. Zero and Negative Exponents LESSON 5-7 Additional Examples (–4) –3 = (–4) 1 –3 = 1 (-4)(-4)(-4) = Simplify the denominator.

5. ALGEBRA READINESS = 243 32 Multiply. = 7 19 32 Simplify. Zero and Negative Exponents LESSON 5-7 Additional Examples 2323 –5 2323 3232 3232 3232 3232 The reciprocol of is. 3232 3232 5 2323 –5 = =   3232

6. ALGEBRA READINESS Simplify: Simplify. 1919 = (–22.4) 0 b. Use the definition of zero as an exponent. = 1 a. 3 –2 Use the definition of negative exponent. Zero and Negative Exponents LESSON 5-7 Additional Examples 132 132 = 3 –2 1 = Simplify. 1 3 =

7. ALGEBRA READINESS Evaluate 4x 2 y –3 for x = 3 and y = –2. Method 1: Write with positive exponents first. 4(3) 2 (–2) 3 = 36 –8 = Simplify. 4x 2 y –3 = Write expression in expanded form. Zero and Negative Exponents LESSON 5-7 Additional Examples Flip negative exponents over to make them positive exponents. 4  x 2  y -3 Substitute 3 for x and –2 for y. 4141 y21y21 1x31x3   = = 4(3)(3) 1(-2)(-2)(-2) Write exponents in expanded form. = –4–4 1212 Make improper fractions into mixed Numbers by dividing bottom into top.

8. ALGEBRA READINESS Evaluate 4x 2 y –3 for x = 3 and y = –2. Method 2: Substitute first. 36 –8 = Simplify. 4x 2 y –3 = Write expression in expanded form and substitute 3 for x and –2 for y.. Zero and Negative Exponents LESSON 5-7 Additional Examples Flip negative exponents over to make them positive exponents. 4  (3) 2  (-2) -3 4141 (3)21(3)21 1 (-2) 3   = = 4(3)(3) 1(-2)(-2)(-2) Write exponents in expanded form. = –4–4 1212 Make improper fractions into mixed Numbers by dividing bottom into top.

9. ALGEBRA READINESS Simplify each expression. 1.6 0 2.4 –2 3. 4. 5. 1 81 2323 – –3 ( ) ( 1313 –4 ) 2323 – –2 ( ) 7 0  5 3 + 1 16 3838 -3 1414 127 Zero and Negative Exponents LESSON 5-7 Lesson Quiz