Page 78 - Math Course 2 (Book 1)

Monomial Expressions: Division

MO. 3 - L2b Let’s Begin

Simplifying Expressions With
Negative Exponents

Negative Exponents
Vocabulary A-Z

Let us learn some vocabulary
Examples

x y
–4 9
Simplify .
Negative exponent z –6
Assume that no denominator is equal to zero.
A negative exponent means how many times to
divide (not multiply) by the number. x y z y Negative Exponent Properties
–4 9
6 9
z –6 = x 4
1
–n
a =
a n z y
6 9
Answer
–1
8 = 1 ÷ 8 = 1/8 = 0.1125 x 4
75p q
–3
5 = 1 ÷ 5 ÷ 5 ÷ 5 = 0.008 Simplify 3 –5
5 –4 –8
15p q r
5 could also be calculated like: Assume that p, q and r are not equal to zero.
–3
3
1 ÷ (5 x 5 x 5) = 1/5 = 1/125 = 0.008
3 –5
75p q 75 p 3 q –5 1
Key Concept 15p q r = 15 p 5 q –4 r –8
5 –4 –8
Group powers with the same base.
Negative Exponent
8
= 5 (p 3–5 ) (q –5(–4) ) (r )
Quotient of Powers and Negative
Words For any nonzero number a and any Exponent Properties
n
integer n, a is the reciprocal of a .
–n
–n
In addition, the reciprocal of a is a n
–1 8
–2
= 5 p q r Simplify.
Symbols For any nonzero number a and any
1 1
1
integer n, a = and = a n = 5 1 r Negative Exponent
– n
8
a n a –n p 2 q
Properties
1 1 1
Example 5 = or = m 3
–2
5 2 25 m –3 5r 8
Answer Multiply fractions.
p q
2
–6 5
–3x y z
Simplify Assume that no denominator is equal to zero.
4 –2 5
30x y z
–6 5
–3x y z = –3 x –6 y 5 z Group powers with the same base.
30x y z 30 x 4 y –2 z 5
4 –2 5
x –10 7 –4
y z
= – Simplify.
10
y 7
Answer = – Negative Exponent Property
10x z
10 4
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