1. Properties and Rules for Exponents Properties and Rules for Radicals
radicand
Exponents and Radicals
base
Properties and Rules for Exponents
Product
Rule
Quotient
Power
Zero Exponent
Negative
Exponent
Power of a
quotient
Bases are different
Bases are the same
Properties and Rules for Radicals
Principal
square root of a
Negative
Cube root of a
nth root of a
nth root of an
if n is an even and positive integer
if n is an odd and positive integer
Product Rule
for Radicals
Quotient Rule
Like radicals
Conjugates
a ≥0
Connections (7.2)
n is the root or
index
m is the power or exponent

2. Rational Exponents Write with exponent notation
Write with radical notation
Simplify if possible

3. Rational Exponents Write with exponent notation
Write with radical notation
Simplify if possible

4. Rational Exponents Write with exponent notation
Write with radical notation
Simplify if possible

5. Rational Exponents Things to remember:
Always write final answer with positive exponents
When using a combination of rules to simplify a problem, there are usually various ways to get the final answer. What is important is that you know and understand each rule individually!

6. Rational Exponents Things to remember:
Always write final answer with positive exponents
When using a combination of rules to simplify a problem, there are usually various ways to get the final answer. What is important is that you know and understand each rule individually!

7. Simplifying using exponent notation
Rewrite with exponent notation and simplify
Write final answer using radical notation
Can we write 9 as a power?
The root for both is still the same

8. Using exponent notation to write as a single radical (same root)
Rewrite with exponent notation
Write exponents with the same common denominator (this will be the root of the radical)
Write final answer using radical notation and simplify if possible
Root is 6
LCD is 6
LCD is 12
Root is 12
LCD is 10
Root is 10