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Apply Exponent Properties
Involving Products
 USE PROPERTIES OF
EXPONENTS INVOLVING
PRODUCTS
 REMEMBER: EXPONENTS LOOK
LIKE THIS: x3
 PRODUCTS INVOLVE
MULTIPLICATION! (x)
Prerequisite Skills
VOCABULARY CHECK
1. Identify the exponent and the base
in the expression 138.
ANSWER
Exponent: 8, base: 13
2. Copy and complete: An expression
that represents repeated multiplication
of the same factor is called a(n) ? .
ANSWER
Power
Prerequisite Skills SKILLS CHECK
Evaluate the expression.
3. x2 when x = 10 4. a3 when a = 3
ANSWER
ANSWER
27
100
5
1
2
3
5. r when r =
6. z when z =
6
2
ANSWER
ANSWER
25
36
1
8
Prerequisite Skills
SKILLS CHECK
Order the numbers from least to greatest.
7. 6.12, 6.2, 6.01
8. 0.073, 0.101, 0.0098
ANSWER
ANSWER
6.01, 6.12, 6.2
0.0098, 0.073, 0.101
Write the percent as a decimal.
9. 4% 10. 0.5% 11. 13.8% 12. 145%
ANSWER ANSWER ANSWER ANSWER
1.45
0.04
0.005
0.138
Prerequisite SkillsSKILLS CHECK
13. Write a rule for the
function.
ANSWER
f (x) = x + 2
Use the product of powers
EXAMPLE 1
property
8
3 5
3
+
5
a. 7 7 = 7
=7
8
2
1
8
2
b. 9 9 9 = 9 9 9
1+8+2
c.
d.
=9
11
=9 6
(– 5)(– 5) = (– 5)1 (– 5)6
1+6
= (– 5)
7
= (–5)
4
3
4+3
7
x x =x =x
for Example 1
GUIDED PRACTICE
Simplify the expression.
2
7
9
3
3
=3
1.
9 10
2. 5 5= 5
2
3
3.(– 7) (– 7) = (–7)
4. x2 x6 x = x9
EXAMPLEUse
2 the power of a power property
a
.
(25)3 = 25
c.
(x2)4
3
= 215
=
x2
= x8
b. [(–6)2]5= (–6)2
5
= (–6)10
4
6]2
[(y
+
2)
d.
= (y + 2)6
= (y + 2)12
2
for Example 2
GUIDED PRACTICE
Simplify the expression.
5. (42)7= 414
7.
3
6
(n )
=
6. [(–2)4]5 = (–2)20
18
n
8. [(m + 1)5]4 = (m + 1)20
Use the power of a product
EXAMPLE 3
property
a. (24
13)8 = 248
138
b. (9xy)2 = (9 x y)2 = 92 x2 y2 = 81x2y2
c. (–4z)2 = (–4 z)2 = (–4)2 z2 = 16z2
d.– (4z)2 = – (4 z)2 = – (42
z2) = –16z2
Use
all
three
properties
EXAMPLE 4
Simplify (2x3)2 x4
(2x3)2 x4 = 22 (x3)2 x4
Power of a product property
= 4 x6 x4
Power of a power property
10
= 4x
Product of powers property
for Examples 3, 4
GUIDED PRACTICE
and 5
Simplify the expression.
9. (42  12)2 = 422  122
2
2
=
9n
(–3n)
10.
11.
(9m3n)4 = 6561m12n4
12.
5  (5x2)4 = 3125x8
Success Criteria:
I can now: Use all three
product properties when
multiplying with exponents