# Elementary Math Chapter 8.2 Negative Exponents and Scientific Notation

## 19 terms · Negative Exponents and Scientific Notation

### Negative Integer Exponent

Let a be any nonzero number and n be a positive integer. Then
a ⁻ⁿ = 1/ aⁿ

7 ⁻³ = 1/ 7³
2 ⁻⁵ = 1/ 2⁵
3 ⁻⁹ = 1/ 3⁹

### Also

1/4 ⁻³ = 1/ 1/4³= 4³

a ³ ⁺ ⁵ = a ⁸

(ab)³

a¹⁵

see next

### 7.2 × 10⁻¹⁴

0. 000000000000072

9.61 × 10⁻⁵

18.9 × 10¹³
or better
1.89 × 10¹⁴

### Ordering of integers

smaller to the left
- 13 〈 -8 〈 -7 〈 0 〈 2 〈 5 〈 11

### - 8 〈 - 5

since
(-8) + 3 = - 5
Also since any negative integer is less than 0
or any positive integer.
-8 must be the smallest

### Properties of Ordering Integers

Let a, b and c be any integers, p a positive integer, and n a negative integer.

### Transitive Property for Less Than

If
a 〈 b and b 〈 c then
a 〈 c.
2 〈 3 and 3 〈 4 then 2 〈 4

### Property of less Than and Addition

if a 〈 b, then a + c 〈 b + c.
2 〈 3, then 2 + 4 〈 3 + 4

### Property of Less Than and Multiplication by a Positive

If a 〈 b, then ap 〈 bp
2 〈 3 , then 2 x 4 〈 3 x 4

### Property of Less Than and Multiplication by a Negative

If a 〈 b, then an 〉 bn.
2 〈 3, then 2 x (-2) 〉 3 x (-2) = -2 〉 -6

### Multiplying an inequality by a negative number "reverses the inequality"

a 〈 b and n 〈 0, then an 〉 bn
2 〈 3, then 2 x (-2) 〉 3 x (-2) = -2 〉 -6