1. Converting Between Radicals & Rational Exponents
Unit 4, Lesson 3
Converting Between Radicals & Rational Exponents

2. 11/30 Do Now *Please start a new Do Now sheet!
Solve for h if V= 1 3 bh
Write a function (y=mx+b) to represent the sequence: -12, , -11.5, …?
The equation y= x represents the value of a work of art from 1964 to What does the number represent?
In 1983, the average price of a home was $50,000. By 2008, the average price of a home is $200,000. What is the annual rate of change?

3. What did we learn last week?
Multiplying exponents, dividing exponents, and negative exponents Let’s review:
y7 * y-3
g4p5 p2
14x-5
(h7d3)(h-2d6)

4. Square Number Also called a “perfect square”
A number that is the square of a whole number
Can be represented by arranging objects in a square.

5. Square Numbers
What do you notice about the table?

6. Perfect Squares
A Perfect Square: is “perfect” because its square root is a whole number.
Can you name any other perfect squares?
Example:
is a perfect square because = 49

7. Non-Perfect Squares
A Non-Perfect Square: is a number whose square root is NOT a whole number.
Example:
is NOT a perfect square because = 40
6.3245…

8. How are radicals & exponents related?
What is a radical?
Includes three separate parts: the index, the radicand, and the actual radical
Identify each part of the following expression:
How are radicals & exponents related?
Inverses!
We can say that radicals “undo” exponents, and exponents “undo” radicals.

9. How to rearrange radical & exponent equations
Remember, 2 × 4=8 can be rearranged into 8 ÷ 4=2
In the same way, we can say
3 8 =2 rearranges into 2 3 =8.
Examples:
Rewrite =4 into an equation with only integers and exponents.
Rewrite 4 3 =64 into an equation that includes a radical.
How did the index, radicand, and base change?

10. Good news! We can rewrite numbers with fractions as exponents using a radical!
Definition of a1/n
If n is a positive integer greater than 1 and 𝑛 𝑎 is a real number, then
𝑎 1/𝑛 = 𝑛 𝑎 .
What this means……..
Let’s look at an example: =
You try: = =
3 8 = =

11. as long as 𝑛 𝑎 is a real number.
MORE good news! We’re not just limited to exponents that are a 1/n fraction!
Definition of am/n
If m and n are positive integers greater than 1, and 𝑚 𝑛 is reduced, then
am/n = 𝑛 𝑎 𝑚 𝑜𝑟 𝑛 𝑎 𝑚
as long as 𝑛 𝑎 is a real number.
For example, 82/3 =
You try:
− =
− =
/2 =

12. EOC Practice
Simplify 3 8𝑥2𝑦3𝑧4

13. EOC Practice
Which expression is equivalent ( 𝑥 1/3 ) −3 ? 𝑥
1 𝑥
1 𝑥9
1 𝑥27

14. Exit Ticket Make sure to put your name on your paper!
If × simplifies to 9, then what do you think
𝑧 × 𝑧 × 𝑧 × 𝑧 simplifies to?