2. 4a 5 (6a 5 ) SOLUTION: Use the Commutative and Associative Properties to group the numbers and variables. The common base is a. Add the exponents.
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1 Simplify using the Laws of Exponents. 1. ( 6) 2 ( 6) 5 The common base is 6. Add the exponents. 2. 4a 5 (6a 5 ) Use the Commutative and Associative Properties to group the numbers and variables. The common base is a. Add the exponents. 3. ( 7a 4 bc 3 )(5ab 4 c 2 ) Use the Commutative and Associative Properties to group the numbers and variables. The common bases are a, b, and c. Remember that a = a 1 and b = b 1. Add the exponents. 4. The common base is 8. Find the difference between the exponents. esolutions Manual - Powered by Cognero Page 1
2 5. Group the numbers and variables of the quotient. The common base is t. Remember that t = t 1. Find the difference between the exponents. Simplify. 6. The common bases are x and y. Find the difference between the exponents. 7. Group the numbers and variables of the quotient. The common base is x. Remember that 3 = 3 1. Find the difference between exponents. Simplify. 8. Group the quotients by the common bases of 4, 5, and 6. Remember that 6 = 6 1. Find the differences between the exponents. Simplify. esolutions Manual - Powered by Cognero Page 2
3 9. The common base is 6. Work in the numerator separately from the denominator. Add the exponents. Find the difference between the exponents. Simplify. 10. Group the quotients by the common bases of 2, 3, and 5. Remember that 3 = ( 3) 1. Find the differences between the exponents. Simplify. 11. The processing speed of a certain computer is instructions per second. Another computer has a processing speed that is 10 3 times as fast. How many instructions per second can the faster computer process? The phrase times as fast indicates multiplication in this situation. The common base is 10. Add the exponents. The faster computer can process instructions per second. esolutions Manual - Powered by Cognero Page 3
4 12. The table shows the seating capacity of two different facilities. About how many times as great is the capacity of Madison Square Garden in New York than a typical movie theater? To find how many times as great, divide 3 9 by 3 5. The common base is 3. Find the difference between the exponents. The capacity of Madison Square Garden is 3 4 or 81 times greater than a typical movie theater. Simplify using the Laws of Exponents. 24. (3x 8 )(5x) Use the Commutative and Associative Properties to group the numbers and variables. The common base is x. Remember that x = x 1. Add the exponents. 25. The common base is h. Find the difference between the exponents g 2 7g 6 Use the Commutative and Associative Properties to group the numbers and variables. The common base is g. Add the exponents. esolutions Manual - Powered by Cognero Page 4
5 27. (8w 4 )( w 7 ) Use the Commutative and Associative Properties to group the numbers and variables. The common base is w. Remember that w is the same as 1w. Add the exponents. 28. ( p )( 9p 2 ) Use the Commutative and Associative Properties to group the numbers and variables. The common base is p. Remember that p is the same as 1p and that p = p 1. Add the exponents. 29. The common base is 2. Remember that 2 = 2 1. Find the difference between the exponents. Simplify. 30. Group the numbers and variables of the quotient. The common base is g. Find the difference between the exponents. Simplify. esolutions Manual - Powered by Cognero Page 5
6 31. Group the quotients by the common bases of 5 and 7. Remember that 5 = 5 1. Find the differences between the exponents. Simplify. 32. Group the quotients by the common bases of 4 and 1. Remember that 4 = 4 1. Find the differences between the exponents. Simplify. esolutions Manual - Powered by Cognero Page 6
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