Here are a few examples of scientific notation, using powers of ten:

one thousand = 1,000
10³ = 10 × 10 × 10 = 10¹ × 10¹ × 10¹ = 10¹⁺¹⁺¹ = 1e3

one million = 1,000,000
10⁶ = 10 × 10 × 10 × 10 × 10 × 10 = 10¹ × 10¹ × 10¹ × 10¹ × 10¹ × 10¹ = 10^1+1+1+1+1+1 = 1e6

one million = one thousand × one thousand
10⁶ = 10³ × 10³ = 10³⁺³ = 1e6

when multiplying powers of ten, add the exponents
10³ × 10² = 10³⁺² = 10⁵ = 1e5

when dividing powers of ten, subtract the exponents
10³ ÷ 10² = 10^3-2 = 10¹ = 10 = 1e1

when raising powers of ten to a power, multiply the exponents
(10⁴)² = 10^{4 × 2} = 10⁸ = 1e8

a negative exponent means that you divide, rather than multiplying, by the powers of ten
10^-4 = 1 ÷ 10⁴ = 0.0001 = 1e-4

negative numbers are smaller than positive ones
-10⁴           <   -10²     <   -10¹   <   -10⁰   <   0   <   10⁰   <   10¹   <   10²   <   10⁴
-10,000     <     -100   <   -10     <   -1       <   0   <   1       <   10     <   100   <   10,000