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Apply Exponent
Properties Involving
Products
February 18, 2014
Pages 489-491
Simplify the expression. Write your answer using exponents.
**To multiply powers having the same base, add the
exponents.
1.
73 75 = 73 + 5 = 78
2.
9 98 92 = 91 98 92
= 91 + 8 + 2
= 911
3.
(– 5)(– 5)6 = (– 5)1 (– 5)6
= (– 5)1 + 6
= (–5)7
4.
x 4 x3 = x4 + 3 = x7
5.
32 37 = 32 + 7 = 39
6.
5 59 = 51 59 = 51 + 9 = 510
7.
(– 7)2(– 7) = (– 7)2 (– 7)1
= (– 7)2+1
= (–7)3
8.
x 2 x6 x
= x2 x6 x1
= x2 + 6 + 1
= x9
Simplify the expression. Write your answer using exponents.
**To find a power of a power, multiply the exponents.
9.
(25)3 = 25
3
10.
= 215
11.
(x2)4 = x2
= x8
[(–6)2]5
= (–6)2
5
= (–6)10
4
12.
[(y + 2)6]2 = (y+ 2)6
= (y + 2)12
2
13.
(42)7 = 42
7
14.
= 414
15.
(n3)6 = n3
= n18
[(–2)4]5
= (–2)4
5
= (–2)20
6
16.
[(m + 1)5]4 = (m + 1)5
4
= (m + 1)20
Evaluate the expression.
**To find a power of a product, find the power of each factor
and multiply.
17.
(9xy)2 = (9 x
y)2 = 92
x2 y2 = 81x2y2
18.
(–4z)2 = (–4 z)2 = (–4)2 z2 = 16z2
19.
– (4z)2 = – (4 z)2 = – (42
z2) = –(16z2)
20. Simplify using all three properties.
(2x3)2 x4
(2x3)2 x4 = 22 (x3)2 x4
Power of a product property
= 4 x6 x4
Power of a power property
= 4x10
Product of powers property
HOMEWORK
Page 492, #6-44, even