Properties of Exponents

Product and Quotient of Powers

100

Simplify (2²) (2⁵)

128

200

Simplify (6⁸)/(6⁶)

36

300

Simplify (r³s⁴) (s²t²)

r³s⁶t²

400

Simplify (a⁸)/(a¹⁷)

a^-9 or 1/(a⁹)

500

Simplify (4⁵e⁴f³) (4^-5e^-6f^-1)

(f²)/(e²)

Power of a Power

100

Simplify (4²)²

256

200

Simplify (u¹¹)¹¹

u¹²¹

300

(q¹⁰)⁰

1

400

Simplify (x^-18)³

x^-54 or 1/x⁵⁴

500

Simplify: ((s⁸)⁴))⁵

s¹⁶⁰

Power of a Product and Power of a Quotient

100

Simplify (a³b⁶)⁴

a¹²b²⁴

200

Simplify (3a / 7b)²

(9a²) / (49b²)

300

Simplify (df)² (gh)⁵

d²f²g⁵h⁵

400

Simplify (p⁵/r⁷)⁹

p⁴⁵/r⁶³

500

Simplify [(4m⁶n¹⁴)/(2m³n⁷)]³

8m²n²

Exponential Functions

100

Which of the following is not an exponential function? a) y= 0.2 * 8^(2) b) y= 4 * x^(2) c) y= 2^(x) d) y= 0.25^(x) + 2

d) y= 0.25^(x) + 2

200

Evaluate the function for x= {-2, -2, 0, 1, 2} y= 0.5^(x)

(-2, 4) (-1, 2) (0, 1) (1, 0.5) (2, 0.25)

300

Evaluate the function for x= {-2, -1, 0, 1, 2} y= -5^(x)

(-2,-0.04) (-1,-0.2) (0,-1) (1,-5) (2,-25)

400

As the value of x increases in the function y=(1/3)^(x) what happens to the value of the function, does it increase/decrease? Give two examples.

(-2,9) and (2, 1/9) shows that as the value of x increases the value of the function decreases.

500

When an exponential function has a positive base, that is less than or equal to 1, does the graph rise or fall from left to right? Give a brief explanation.

It falls. When 0

Exponential Growth and Decay

100

Exponential growth can be modeled by the function y=a*b^{x. What does the b signify?}

b is the growth factor and is greater than one.

200

Suppose that the population of a city was 8,000 six years ago, but since then it has been declining at an average rate of 0.75% per year. Write an equation to find the population after x years.

y=8,000(1-0.0075)^x

300

The value of a new car decreases exponentially at a rate of 15% per year. A new has an initial value of $24,000. What is the value of the car after 5 years?

Value of the car after 5 years: $10,648.93

400

20% of a particular medicine is absorbed by the bloodstream every hour. A patient takes a 40 milligram dose of this medicine at 9 A.M. How many miligrams of medicine are absorbed in the bloodstream at 2 P.M?

13.11 milligrams of medicine are absorbed.

500

Determine whether following points represent a linear, absolute value, or exponential function. Give a brief explanation as to why. (1,3) (2,9) (3,27) (4,81)

Exponential because there is a common ratio between the values.