University:
Jackson College
Course:
MAT-039 | Beginning Algebra
Academic year:

2021
Views:

262

Pages:

5
Author:

Veggianl5om

Chapter 3 – Powers and Exponents LESSON 4: EXPONENT LAWS WITH VARIABLES Review of Exponent Laws 1. 2. 3. 4. 5. When multiplying two powers together with the same base, ADD the exponents When dividing two powers with the same base, SUBTRACT the exponents To raise a power to a power, MULTIPLY the exponents When a product is raised to an exponent, you can rewrite each factor in the product with the same exponent. When a quotient is raised to an exponent, you can rewrite each number in the quotient with the same exponent. 6. When the exponent of a power is zero, the value of the power is ONE (as long as the base is not zero). Ex.1: Rewrite as a single power a) t 7 ⋅ t 12 b) a ⋅ a 4 ⋅ a 5 ⋅ a16 Ex.2: Rewrite as a repeated multiplication then simplify a) 2 x 2 ⋅ 3 x 3 b) 5 x ⋅ (−3 x 3 ) Rule: Multiply coefficients together and then add the exponents of powers with the same base. Ex.3: Simplify a) (5 xy 2 )(7 x 3 y 2 ) b) − 7b 2 a ⋅ 2a 2 b ⋅ 5a 3 Reducing algebraic terms is similar to reducing fraction. Look for common factors in the numerator and denominator. Ex.4: Simplify a) 7 7 b) 3 21 c) a3 a5 d) 6x3 y 30 y 2 x Ex.5: Rewrite as a repeated multiplication then simplify ( ) a) x 2 ( ( ) 3 c) x 3 y 2 b) 4x 2 3 ) 2 Raise the coefficients to the power and apply the power to one variable at a time by multiplying exponents Ex.6: Simplify ( a) 11a 2 b 3 c ) 2 ( b) − 5xy 2 ) 4 ( c) − ab 2 c 3 ) 3 Chapter 3 Powers and Exponents – Worksheets DAY 4: EXPONENT LAWS WITH VARIABLES 1. a) a 9 ⋅ a 20 e) (−3a 2 )(−4a 7 ) b) c 9 ⋅ c ⋅ c 4 ⋅ c 21 c) (b 3 )(b10 ) d) (3a 2 )(6a10 ) f) − 12 x 2 (−5 x10 ) g) (−4 x 5 )(7 x 7 ) h) a 2 (a 7 )(−3a ) b) (−mb 2 )(−3m 2 ) c) 3 x(−5 x 2 b 2 ) d) 2a 5 (−a 2 )(−5a ) e) (−2a 3 x)(4a 2 x 7 ) f) − 2ab 2 (−ab)(b 7 ) g) (−2ax 2 )(−6a 4 )(−3 x10 ) h) b 7 a 4 (−100ca 3 )(−a 2 bc) i) (20a )(−ax 2 )(−4a 2 x 2 ) 2. a) (−8 xy 2 )(− x 4 y 10 ) 3. a) f) bc c b) b4 b c) a8 a2 d) a6 y a2 y9 e) − 4x 2 12 x 5 a10 y 6 a 2c 2 g) − 4x5 y − 20 x 5 h) 15ab 9 − 9a 7 b10 i) − 5 x12 − 30 x14 j) x12 − x 20 4. a) (c 2 ) 3 e) (h10 ) 20 5. a) ( x 3 y ) 4 e) (4a 3 m 2 ) 2 b) (a 3 ) 2 c) ( y 5 ) 3 d) ( f 7 ) 7 f) (−2w 4 ) 3 g) (−2 x 2 ) 3 h) (− x 4 ) 3 b) (af 2 ) 5 c) (−3a 2 b 3 ) 3 d) (2 x 2 yz 3 ) 4 f) (5a 2 b 3 ) 3 g) (3a 3b 2 ) 3 h) (−3 x 3 y 4 z 2 ) 3 ANSWER KEY Day 4: Exponent Laws with Variables 1. a) a 29 b) c 35 c) b13 g) − 28x12 h) − 3a10 b) 3b 2 m 3 c) − 15b 2 x 3 2. a) 8 x 5 y 12 g) − 36a 5 x12 h) 100a 9 b 8 c 2 i) 80a 4 x 4 3. a) b y 5 4. a) c 6 g) − 8x 6 5. a) x12 y 4 g) f) 125a 6 b 9 b) b 3 c) a 6 −5 3a 6 b b) a 6 h) − x12 b) a 5 f 10 1 6x 2 c) y 15 h) g) 27 a 9 b 6 i) d) 18a12 e) 12a 9 f) 60x12 d) 10a 8 e) − 8a 5 x 8 f) 2a 2 b10 a4 y8 1 j) − 8 x d) f 49 e) − d) 1 3x 3 e) h 200 c) − 27 a 6 b 9 d) 16 x 8 y 4 z 12 e) 16a 6 m 4 h) − 27 x 9 y 12 z 6 f) a8 y 6 c2 f) − 8w12 f) 125a 6 m 4