1. ALGEBRA II HONORS/GIFTED - SECTION 6-1 (Roots and Radical Expressions)
4/20/2019
ALGEBRA II HONORS/GIFTED @
SECTION 6-1 : ROOTS and RADICAL EXPRESSIONS

2. First, some review from Algebra I.
Simplify each expression. Leave only positive exponents in your answer.
1) (2a3)(5a4)
3) (3x-4y3)2
ANSWER : 10a7
ANSWER : 9y6 / x8
2) (-3x2)(-4x-2)
4) (2x3y7)-2
ANSWER : 12
ANSWER : 1 / 4x6y14

3. 5) 7) 6) 8) ANSWER : r5 / 81s10 ANSWER : 5t4 / rs2 ANSWER : t12 / r

4. PROPERTIES OF EXPONENTS
PRODUCT OF POWERS : am • an = am+n
POWER OF A POWER : (am)n = amn
POWER OF A PRODUCT : (ab)m = ambm
POWER OF A MONOMIAL : (ambm)p = ampbmp
QUOTIENT OF POWERS :
ZERO EXPONENT : a0 = 1 (a ≠ 0)
NEGATIVE EXPONENTS :

5. NOTE : The principal square root is the positive root.
Determine the Real square roots.
9) 121
11)
ANSWERS : 11 and -11
ANSWER : none
NOTE : The principal square root is the positive root.
What are the Real
fourth roots of ?
10)
ANSWERS : 5 / 7 and -5 / 7
ANSWERS : 2 / 3 and -2 / 3

6. PROPERTY FOR nth ROOTS of nth POWERS
Find each square root.
13)
14)
ANSWER : 7
ANSWER : 7
PROPERTY FOR nth ROOTS of nth POWERS

7. Simplify each expression. Use absolute value symbols when needed.
15)
19)
17)
ANSWER : 5a2
ANSWER : abs(p3q)
ANSWER : p4q5
16)
18)
ANSWER : 7(abs(x))• sqrtx
ANSWER : abs(p3) • q4