7­3 More Multiplication Properties of Exponents simplify ​
(verb) sim pluh fy Related Words: ​
simple (adjective), simplified (adjective, verb) Main Idea:​
You simplify an expression to make it less complicated. Definition:​
To simplify an expression means to replace it with a simplified form. Simplify each expression. 10
( )
8
A.) (n4 )
B.) x
2
5
− 12
( )
C.) x
3
5
0 1
D.) (z 8 ) z 2
1
E.) (c3 ) 9
0
(d ) 3
−1
F.) (m3 )
(x )
1
3
1
4
Essential Understanding​
You can use properties of exponents to simplify a power raised to a power or a product raised to a power. you can use repeated multiplication to simplify a power raised to a power. 2
(x5 ) = x5 • x5 = x5+5 = x5•2 = x10 2
Notice that (x5 ) = x5•2 . Raising a power to a power is the same as raising the base to the product of the exponents. Simplify each expression. G.) (7a)
−2
1
−
H.) (36g4 ) 2
−3
( )
I.) 2y
7
9
1
2
J.) (y2 z −3 ) 6 (y3 ) 2 6
3
( )k K.) 4j k 2j
11
5
(
2 4
L.) 2j k
−5
6
) (k j ) −1 7
You can use the property of raising a product to a power to solve problems involving scientific notation. For example, to simplify the (
8
expression 3 × 10
2
)
8
, you raise both 3 and 10 to the second power. Then multiply the two powers. Simplify. Write each answer in scientific notation. (
M.) 4 × 102
5
) (
N.) 2 × 10−3
3
) (
O.) 6.25 × 10−12
−2
)
(
8
P.) 2.37 × 10
3
)