Writing Radicals in Rational Form

1
Writing Radicals in Rational Form

• Section 10.2

2
DEFINITIONS

• Base The term/variable of which is being raised
  upon
• Exponent The term/variable is raised by a term.
  AKA Power

EXPONENT
BASE
3
THE EXPONENT
4
NTH ROOT RULE

• M is the power (exponent)
• N is the root
• A is the base

5
RULES

• Another way of writing is 251/2.
• is written in radical expression form.
• 251/2 is written in rational exponent form.
• Why is square root of 25 equals out of 25 raised
  to ½ power?

6
EXAMPLE 1

• Evaluate 43/2 in radical form and simplify.

7
EXAMPLE 1

• Evaluate 43/2 in radical form and simplify.

8
EXAMPLE 2

• Evaluate 41/2 in radical form and simplify.

9
YOUR TURN

• Evaluate (27)2/3 in radical form and simplify.

10
EXAMPLE 3

• Evaluate 274/3 in radical form and simplify.

Use calculator to check
Hint Remember, the negative is OUTSIDE of the
base
11
EXAMPLE 4

• Evaluate in radical form and simplify.

12
NTH ROOT RULE

• M is the power (exponent)
• N is the root
• A is the base
• DROP AND SWAP

13
EXAMPLE 5

• Evaluate (27)2/3 in radical form and simplify.

14
EXAMPLE 6

• Evaluate (64)2/3 in radical form and simplify.

15
YOUR TURN

• Evaluate in radical form and simplify.

16
PROPERTIES OF EXPONENTS

• Product of a Power
• Power of a Power
• Power of a Product
• Negative Power Property
• Quotient Power Property

17
EXAMPLE 7

• Simplify
• Saying goes BASE, BASE, ADD
• If the BASES are the same, ADD the powers

18
EXAMPLE 8

• Simplify

19
YOUR TURN

• Simplify

20
EXAMPLE 9

• Simplify
• Saying goes POWER, POWER, MULTIPLY
• If the POWERS are near each other, MULTIPLY the
  powers usually deals with PARENTHESES

21
EXAMPLE 10

• Simplify

22
YOUR TURN

• Simplify

23
EXAMPLE 11

• Simplify
• Saying goes When dividing an expression with a
  power, SUBTRACT the powers.

24
EXAMPLE 12

• Simplify

25
EXAMPLE 13

• Simplify