Sutz Properties of Exponents & Exponential Functions

Multiplying and Dividing

100

Solve using the properties of exponents: 

c^10/c^5

c⁵

200

Simplify using Properties of Exponents: x³*x⁵*y³*z⁰

x⁸y³

300

Simplify using Properties of Exponents: d²² · d¹²

d³⁴

400

Simplify using Properties of Exponents: 

(x^25*y^-5) / (x^-13*y^5)

x³⁸/y¹⁰

500

Simplify using Properties of Exponents: 

(2y^(0)x^(2)2y^2)/(x^3*y^2)

4/x

Power of a Power

100

Anything to the power of 0 equals....

1

200

Simplify using Properties of Exponents: (x⁴)³

x¹²

300

Simplify using Properties of Exponents: (2p⁵)³

8p¹⁵

400

Simplify using Properties of Exponents: (z⁴)^-4

1/z^16

500

Simplify using Properties of Exponents: (x(m^-2)⁴)³

x^3/m^24

Properties of Exponents

100

Solve using properties of exponents? (x³y⁴)(x^-2y^-1)

xy³

200

Simplify using Properties of Exponents: (c²)³

c⁶

300

Simplify using Properties of Exponents: 3x²y^-26

(18x^2)/y^2

400

Simplify using Properties of Exponents:

x^-2/x^-2

1

500

Simplify using Properties of Exponents: (r¹⁰)(r^-2)/ (r⁵)²

1/(r^2)

Exponential Functions

100

What is the starting amount of this function?

f(x) = 10(2)^x?

10

200

Is this function growing or decaying?

f(x) = 0.5(1.5)^x

Growing

300

What is the growth rate of this function?

f(x) =(2)^x

Growth Rate = 1 or 100%

400

What is the output when x = 3?

f(x) = 5(2)^x

40

500

What is the equation of this function?

x    -2    -1    0    1      2

y    27    9    3   1/3   1/9

f(x) = 1/3(3)^x

Mixed

100

A rocket ship takes off starting 25 feet off the ground. It accelerates triple its distance every minute. 

What is the equation that models this situation?

f(x) = 25(3)^x

200

Simplify the following expression to only contain positive exponents: 

b^-3/a^-3

a^3/b^3

300

What is the growth rate of this function?

f(x) = 1.25(1.25)^x

25%

400

Simplify the following expression to only contain positive exponents: (a⁷ * a⁰ * a^-5)^-2

1/a^4

500

What is the rate of decay for this function?

f(x) = .05(.05)^x

95%