{5.2} SIMPLIFY with the properties of rational exponents. *Quotient of powers: 5 / (5 1/3)

5 / (5 1/3)= 51/ (51/3) = 5(1 - 1/3) = 5(3/3 - 1/3)=52/3

{5.1} APPROXIMATE the expression with Rational Exponents. 1. ( ∜7 )3

( ∜7 )3 = 73/4 ≈ 4.30 >>> ( ∜7 )3 = 4.30, ( ∜7 )3 = 4.30 >>> ( ∜7 )3 = 4.30

{5.2}SIMPLIFY with the property of radicals. *Quotient of property: ∜2 / ∜512

∜2 / ∜512= ∜2 / 512 = ∜256 = 4

{5.1} FIND how many real nth roots of a will come from evaluating 1. n=4, a=81

n=4, a=81>n=4,even & a=81, 34 = 81 & (-3)4 = 81 > ±∜81 = ±3

{5.1} EVALUATE the expression. 1. 32-3/5

32-3/5 = 1 / 323/5 = 1 / 23 = 1/8 >>> 32-3/5 = 1/8, 32-3/5 = 1/323/5 = 1 / (5 'sqrt.' 32)3 = 1/23 = 1/8 > = 1/8

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alg.2 {Rational Exponents & Radical Functions} chp. 5

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A math Quizquiz to review the basics of algebra 2, chapter 5: "Rational Exponents & Radical Functions".

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Questions 6

Answers

1
{5.2} SIMPLIFY with the properties of rational exponents. *Quotient of powers: 5 / (5 ^1/3)
5 / (5 1/3)= 51/ (5+1/3) = 1(1 - 1/3) = 1(1/3+ 3/3)=52/3
5 / (5 1/3)= 51/ (51/3) = 5(1 - 1/3) = 5(3/3 - 1/3)=52/3
-5 / (5 1/3)= -51/(51/3) =-5(1 - 1/3) = 5(3/3 -1/3) = -52/3
5 / (5 -1/3)=51/ (5-1/3) =5(1 - 1/3) =5(-3/3 - 1/3)=5-2/3
2
{5.1} APPROXIMATE the expression with Rational Exponents. ^1. ( ∜7 )³
( ∜7 )3 = 73/4 ≈ 4.30 >>> ( ∜7 )3 = 4.30
( ∜7 )3 = 4.30 >>> ( ∜7 )3 = 4.30
( ∜7 )-3 = 7-3/4 ≈ -4.30 >>> ( ∜7 )-3 = -4.30
( ∜7 )3 = 37/4 ≈ 3.40 >>> ( ∜7 )3 = 3.40
3
{5.1} FIND the nth root of a. ^1. n= 3, a= -125
∛125 = -3 -1251/5 = 3
∛125 = -5 -1251/3 = 5
∜125 = -5 -1251/4 = 5
∛-125 = -5 -1251/3 = -5
4
{5.2}SIMPLIFY with the property of radicals. *Quotient of property: ∜2 / ∜512
∜2 / ∜-512= ∜2 / -512 = ∜-256 = -4
∜512 / ∜-2= ∜512 / -2 = ∜-256 = -4
∜2 / ∜5122 = ∜2 / 5122 = ∜2562 =-16
∜2 / ∜512= ∜2 / 512 = ∜256 = 4
5
{5.1} FIND how many real nth roots of a will come from evaluating ^1. n=4, a=81
n=81, a=4 >n=81,odd & a=4, 22 =4 > ∜81 = ±3
n=4, a=81>n=4,even & a=81, 34 = 81 & (-3)4 = 81 > ±∜81 = ±3
n=4, a=81>n=4,even & a=81, (-3)4 = 81 > -∜81 = -3
n=4, a=81> n=4, odd & a=81, 34 = 81 > ∜81 = 3
6
{5.1} EVALUATE the expression. ^1.32^-3/5
32-3/5 = 1 / 323/5 = 1 / 23 = 1/8 >>> 32-3/5 = 1/8
323/-5 = 1 / 323/-5 = 1 / 23 = 1/8 >>> 323/-5 = 1/8
32-3/5 = 32 / 13/5 = 2 /13 = 1/8 >>> 32-3/5 = -1/8
32-3/5 = 1/323/5 = 1 / (5 'sqrt.' 32)3 = 1/23 = 1/8 > = 1/8

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