Review: Base and Exponent
Integer Exponents Rules
OBJECTIVE: TO USE
EXPONENT RULES TO
SIMPLIFY
EXPRESSIONS .
Identify the base and the exponent in each of the
following. Pay close attention to parenthesis.
EXAMPLES
A) 32
B) -32
7
C) (-3)
D) x4
9
E) (-x)
F) -x3
Review: Solutions
Identify the base and the exponent in each of the
following. Pay close attention to parenthesis.
EXAMPLES
A) 32
B) -32
7
C) (-3)
D) x4
9
E) (-x)
F) -x3
Examples
Evaluate.
A) 32
B) -32
C) (-3)2
Answers
A) base = 3, exponent = 2
C) base = -3, exponent = 7
E) base = -x, exponent = 9
B) base = 3, exponent = 2
D) base = x, exponent = 4
F) base = x, exponent = 3
Examples -- Solutions
Evaluate.
A) 32
B) -32
C) (-3)2
Product Rule (like bases)
am · an = am + n
In other words, if multiplying with the same base,
add the exponents.
Answers
A) (3)(3) = 9
B) - (32) = - (3)(3) = - 9
C) (-3)(-3) = 9
EXAMPLES
G) x2(x)
H) 23(22)
I) (-3)3(-3)2
1
Product Rule Solutions
Power to a Power
am · an = am + n
( am)n = amn
In other words, if multiplying with the same base,
When a power is raised to a power, multiply the
add the exponents.
EXAMPLES
G) x2(x)
H) 23(22)
EXAMPLES
exponents.
I) (-3)3(-3)2
J) (x5)2
K) (y4)3
Answers
G) x2+1 = x3
H) 23+2 = 25 = 32
I) (-3)3+2 = (-3)5 = -243
Power to a Power Solutions
Product to a Power
( am)n = amn
(ab)n = an bn
When a power is raised to a power, multiply the
When a product is raised to a power, raise each
exponents.
EXAMPLES
J) (x5)2
EXAMPLES
factor in the product to the power.
K) (y4)3
L) (2x2)2
M) (3a3b4)2
Answers
J) x 5 · 2 = x10
K) y 4 · 3 = y12
Product to a Power Solutions
(ab)n = an bn
When a product is raised to a power, raise each
factor in the product to the power.
EXAMPLES
L) (2x2)2
M) (3a3b4)2
Answers
L) 22 (x2)2 = 4x4
M) 32 (a3)2 (b4)2 = 9(a3·2)(b4·2)= 9a6b8
Quotient to a Power
n
an
a
  = n
b
b
In other words, when raising a fraction to a power,
raise the numerator to the power and the
denominator to the power.
2
Examples Solutions
Examples
 a3 
N)  2 
b 
3
 x5 y 
O)  2 6 
m n 
4
 a3 
N)  2 
b 
3
 x5 y 
O)  2 6 
m n 
4
ANSWERS
N)
More Examples
P) (c2)3 (3c5)4
Q) (6mn)3(5m3)2
R) (2a3)5(3ab2)3
(a 3 )3 a 3⋅3 a 9
=
=
(b 2 )3 b 2 ⋅3 b6
O)
( x 5⋅ 4 y1⋅ 4 ) x 20 y 4
=
(m 2⋅ 4 n 6⋅ 4 ) m8 n 24
More Examples SOLUTIONS
P) (c2)3 (3c5)4
= c6(34 c20)
= c6(81 c20)
=81 c26
Q) (6mn)3(5m3)2
= (63m3n3)(52m6)
=(216 m3n3 )(25m6)
= 5400m9n3
R) (2a3)5(3ab2)3
(32a15)(27a3b6)
864a18b6
3