1-3 Multiply and Divide Monomials
Simplify using the Laws of Exponents.
2
5
1. (–6) • (–6)
SOLUTION: The common base is –6. Add the exponents.
5
5
2. –4a (6a )
SOLUTION: Use the Commutative and Associative Properties to group the numbers and variables. The common base is a. Add
the exponents.
4
3
4 2
3. (–7a bc )(5ab c )
SOLUTION: Use the Commutative and Associative Properties to group the numbers and variables. The common bases are a, b,
1
1
and c. Remember that a = a and b = b . Add the exponents.
4. SOLUTION: The common base is 8. Find the difference between the exponents.
5. SOLUTION: 1
Group the numbers and variables of the quotient. The common base is t. Remember that t = t . Find the difference
between the exponents. Simplify.
eSolutions Manual - Powered by Cognero
Page 1
The common base is 8. Find the difference between the exponents.
1-3 Multiply and Divide Monomials
5. SOLUTION: 1
Group the numbers and variables of the quotient. The common base is t. Remember that t = t . Find the difference
between the exponents. Simplify.
6. SOLUTION: The common bases are x and y. Find the difference between the exponents.
7. SOLUTION: 1
Group the numbers and variables of the quotient. The common base is x. Remember that 3 = 3 . Find the difference
between exponents. Simplify.
8. SOLUTION: 1
Group the quotients by the common bases of 4, 5, and 6. Remember that 6 = 6 . Find the differences between the
exponents. Simplify.
eSolutions Manual - Powered by Cognero
9. SOLUTION: Page 2
1-3 Multiply and Divide Monomials
9. SOLUTION: The common base is 6. Work in the numerator separately from the denominator. Add the exponents. Find the
difference between the exponents. Simplify.
10. SOLUTION: 1
Group the quotients by the common bases of –2, –3, and –5. Remember that –3 = (–3) . Find the differences
between the exponents. Simplify.
11
11. The processing speed of a certain computer is 10 instructions per second. Another computer has a processing
3
speed that is 10 times as fast. How many instructions per second can the faster computer process?
SOLUTION: The phrase times as fast indicates multiplication in this situation. The common base is 10. Add the exponents.
The faster computer can process 10
14
instructions per second.
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?
SOLUTION: eSolutions Manual - Powered by Cognero
9
5
To find how many times as great, divide 3 by 3 . The common base is 3. Find the difference between the
exponents.
Page 3
The phrase times as fast indicates multiplication in this situation. The common base is 10. Add the exponents.
1-3 Multiply and Divide Monomials
14
The faster computer can process 10 instructions per second.
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?
SOLUTION: 9
5
To find how many times as great, divide 3 by 3 . The common base is 3. Find the difference between the
exponents.
4
The capacity of Madison Square Garden is 3 or 81 times greater than a typical movie theater.
Simplify using the Laws of Exponents.
8
24. (3x )(5x)
SOLUTION: Use the Commutative and Associative Properties to group the numbers and variables. The common base is x.
1
Remember that x = x . Add the exponents.
25. SOLUTION: The common base is h. Find the difference between the exponents.
2
26. 2g • 7g
6
SOLUTION: Use the Commutative and Associative Properties to group the numbers and variables. The common base is g. Add
the exponents.
4
7
27. (8w )(–w )
eSolutions Manual - Powered by Cognero
SOLUTION: Use the Commutative and Associative Properties to group the numbers and variables. The common base is w.
Page 4
1-3 Multiply and Divide Monomials
4
7
27. (8w )(–w )
SOLUTION: 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.
2
28. (–p )(–9p )
SOLUTION: Use the Commutative and Associative Properties to group the numbers and variables. The common base is p .
1
Remember that –p is the same as –1p and that p = p . Add the exponents.
29. SOLUTION: 1
The common base is 2. Remember that 2 = 2 . Find the difference between the exponents. Simplify.
30. SOLUTION: Group the numbers and variables of the quotient. The common base is g. Find the difference between the exponents.
Simplify.
31. SOLUTION: 1
Group the quotients by the common bases of 5 and 7. Remember that 5 = 5 . Find the differences between the
exponents. Simplify.
eSolutions Manual - Powered by Cognero
Page 5
1-3 Multiply and Divide Monomials
31. SOLUTION: 1
Group the quotients by the common bases of 5 and 7. Remember that 5 = 5 . Find the differences between the
exponents. Simplify.
32. SOLUTION: 1
Group the quotients by the common bases of 4 and –1. Remember that 4 = 4 . Find the differences between the
exponents. Simplify.
eSolutions Manual - Powered by Cognero
Page 6