Sect 5.1 - Exponents: Multiplying And Dividing Common Bases Worksheet With Answers Page 2
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1
2
3
4
5
6
741
Solution:
2
a)
(– 4)
= (– 4)(– 4) = 16
2
= – 4 • 4 = – 16
b)
– 4
3
c)
(– 0.5)
= (– 0.5)(– 0.5)(– 0.5) = – 0.125
3
= – 0.5 • 0.5 • 0.5 = – 0.125
d)
– 0.5
Evaluate each expression for a = 3 and b = – 4:
2
2
Ex. 3a
5a
Ex. 3b
(5a)
2
2
Ex. 3c
5ab
Ex. 3d
(b + a)
Solution:
2
a)
5a
(replace a by (3))
2
= 5(3)
(#2-exponents)
= 5(9)
(#3-multiply)
= 45
2
b)
(5a)
(replace a by (3))
2
= (5(3))
(#1-parenthesis, #3-multiply)
2
= (15)
(#2-exponents)
= 225
2
c)
5ab
(replace a by (3) and b by (– 4))
2
= 5(3)(– 4)
(#2-exponents)
= 5(3)(16)
(#3-multiply)
= 240
2
d)
(b + a)
(replace a by (3) and b by (– 4))
2
= ((3) + (– 4))
(#1-parenthesis, #4-add)
2
= (– 1)
(#2-exponents)
= 1
Concept #3
Multiplying and Dividing Common Bases
Simplify the following:
5
• x
3
Ex. 4
x
Solution:
5
3
Write x
and x
in expanded form and simplify:
5
• x
3
= (x • x • x • x • x) • (x • x • x) = x • x • x • x • x • x • x • x = x
8
x
.
Notice that if we add the exponents, we get the same result:
5
• x
3
5 + 3
8
x
= x
= x
. This introduces our first property for
exponents.
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