1. Powers and Radicals without Calculators (6.5)
Using a factor tree when your calculator goes on the fritz

2. A little review
Let’s look again at yesterday’s exponential problems we simplified:
(6x5)(3x-2)
(5x-4)(2x-3)
(-2x2)3(3x-1y2)4
(x-1y-4z)/(x-2yz-3)
(3x-1/2)(4x2/3)
(3758x89)(3758x-89)
(u3.7p4.8)/(u-2.9p1.8)

3. A POD warm-up Rewrite each of the following using a radical sign: 81/3
2431/5
Can you figure out what they equal without using a calculator?

4. Let’s look more closely
81/3
What is the factor tree for 8?
How could we use that to find the final answer?

5. Let’s look again more closely
2431/5
What is the factor tree for 243?
How can we use it to find a final answer?

6. Now try this
Use a factor tree to find 2561/4.
Use it to find 641/3.

7. Let’s mix it up a bit What is 2431/5? What would 2433/5 equal then?

8. You design one
Write a power expression with a fraction exponent that equals 2.
We’ve seen that 81/3 will do this. Any others?
How about one that equals 4?

9. Signs -2431/5 equals -3 2561/4 equals 4 641/3 equals 4
So, we can take:
the even root of a positive number.
the odd root of a positive number.
the odd root of a negative number.
But we cannot take:
the even root of a negative number (remember finding the square root of a negative number?)