1. Rational and Irrational Numbers and Their Properties (1.1.2)
September 6th, 2017

2. Solving Exponential Equations
General
Example
Power
Root
Rational Exponent-Case 1
Rational Exponent-Case 2

3. Ex. 1: Simplify
Why does it make sense to add the exponents when multiplying variables of the same base?

4. Ex. 2: Simplify
Why does it make sense to subtract the exponents when dividing variables of the same base?

5. Ex. 3: Solve the equation

6. Ex. 4: Solve the equation

7. How can you determine whether the sum or product of two numbers will be rational or irrational?

8. Ex. 1: Are the following sums and products rational or irrational?
a) b)
c) d)
e) f)
g) h)

9. Do you see any pattern in what makes the result rational or irrational?

10. Rational x Rational = Rational
RULE
EXAMPLE
Rational
Rational x Rational = Rational
Irrational
Irrational

11. Is the sum or product of two irrational numbers always irrational?

12. Ex. 2: Are the following sums and products rational or irrational?
a) b)
c) d)