New News Algebra #6

Exponents & Scientific Notation

Idea: Exponent

The number of times a number is multiplied by itself

e.g. 2^3=8

e.g. 3^2=9

Sub-idea 1: Multiplying Exponents

x^a * x^b = x^a+b

e.g. 2^3*2^4=2^3+4=2^7

Sub-idea 2: Raising Exponents

(x^a)^b = x^ab

e.g. (2^2)^3=(2*2)(2*2)(2*2)=2^2*3=2^6

Sub-idea 3: Dividing Exponents

x^a / x^b = x^a-b (x≠0)

e.g. 2^10÷2^5=2^10-5=2^5

Sub-idea 4: Power of Zero

x^0= 1 (x≠0)

Note: 0^0 is undefined

e.g. 2^5÷2^5=2^5-5=2^0=1

e.g. 30^4÷30^4=30^4-4=30^0=1

Sub-idea 5: Negative Exponents

If x≠0, then x^-a=1/x^a

e.g. 2^-3=1÷2^3=1/8

Sub-idea 6: Fraction Powers

x^1/a=a√x

e.g.2^1/2=√2

e.g. 8^1/3=3√8=2

Idea 2= Scientific Notation

a way of representing super large numbers

for example, visualize the following:

1.1400000=1.4*10^6

2.2436781000=2.436781*10^9