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

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

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

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 :

NOTE : The principal square root is the positive root. Determine the Real square roots. 9) 121 11) -0.81 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

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

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