Rational and Irrational Numbers and

Their Properties (1.1.2)

Rational and Irrational Numbers and

Their Properties (1.1.2)September 9th, 2015September 9th, 2015

Solving Exponential Equations

GeneralGeneral ExampleExample

PowerPower

RootRoot

Rational Rational Exponent-Case Exponent-Case

11

Rational Rational Exponent-Case Exponent-Case

22

xa =b→ xaa = ba

→ x= ba

x3 =64 →

xa =b→ xa( )a=ba

→ x=ba

x4 =3→

xmn =b→ x

mn( )

nm

=bn

m

→ xm

ngnm =bn

m→ x=bn

m

x32 =27 →

xmn =b→ xmn( )

n

=bn → xm =bn

→ xmm = bnm → x= bnm

x23 =25 →

Ex. 1: Simplify . n45 ⋅n

23

Why does it make sense to add the exponents when multiplying variables of the same base?

Ex. 2: Simplify .a32

a45

Why does it make sense to subtract the exponents when dividing variables of the same base?

Ex. 3: Jodie has decided she wants to buy the new 18-karat gold iWatch for $15,000 within the next 5 years. She currently has $12,000 and needs to know the minimum interest rate at which she must invest her money to reach her goal. She realizes that she can determine the amount of money (y) in her account at any time with the equation , where t is the time in years, c is the initial investment, and x is the interest rate plus 1. What is the interest rate she needs?

y=c(x)t

Ex. 4: Solve the equation . x23 =36