1. 1.4 Rational Exponents

2. Essential standard
I can convert radical expressions and rational exponents
I can use properties of exponents to combine radicals

3. RATIONAL EXPONENTS
Any radical expression can be written in an equivalent form using fractional (rational) exponents instead of the radical sign.
36 = = =
The index is the denominator of the exponent.
The exponent is the numerator of the exponent.

4. PROBLEM 1 What is the simplified form of each expression? A) 216 1 3

6. PROBLEM 2 Convert between exponential and radical form.
A) What is 𝑥 in radical form?
B) What is 𝑎 5 and 5 𝑏 3 in exponential form?

8. POWER RULES
The main advantage of changing a radical into exponential form is it allows the use of power rules, which are shortcuts for exponents.

9. PROBLEM 3
Rewrite in radical form
4 𝑥 𝑥 2

11. SIMPLIFYING RATIONAL EXPONENTS
The index is the denominator of the exponent.
The exponent is the numerator of the exponent.
With a rational exponent, there are two operations to perform instead of one.
means we must raise 4 to the third power ( 4 3 ) and square root it ( = 4 )

12. PROBLEM 4
What is − in simplest form?

14. PROBLEM 5
Simplify each expression.
A) 𝑥 ⋅ 𝑥 B) 𝑥 ÷ 𝑥 5 14

15. GOT IT? below Simplify each expression.
A) 𝑦 ⋅ 𝑦 B) 𝑥 ÷ 𝑥 1 3

16. Essential standard
I can convert radical expressions and rational exponents
I can use properties of exponents to combine radicals