Exponent Rules and Exponential Functions

Zero and Negative Exponents - Basic

100

x⁰

What is 1?

200

-16⁰

What is -1?

300

16^-1

What is 1/16?

400

(1/16)^-1

What is 16?

500

(x^-3)(x³)

No calculator

What is 1?

Exponents with Multiplication

100

b⁷ (b¹³)

What is b²⁰?

200

(8d⁴)(4d⁷)

What is 32d¹¹?

300

Simplify then evaluate: 

2³ * 2²

What is 2⁵ = 32?

400

x^-9 * x³ * x²

What is x^-4 = 1/x⁴?

500

(7p⁴)(5p⁹)(2q^-7)

What is 70p¹³/q⁷?

Power to a Power Rules

100

(x⁵)²

What is x¹⁰?

200

(2^-3)⁴

What is 2¹² = 1/(2¹²)?

300

(4a⁵)³

What is 64a¹⁵?

400

(m^-3*n⁴)^-4

What is m¹² * n^-16 = m¹²/n¹⁶?

500

(4x⁴)² (2xy³)³

What is 128x¹¹y⁹?

Division with Exponents

100

c¹⁶/c⁹

What is c⁷?

200

Simplify then evaluate: 

3⁷/3⁴

What is 3³ = 27?

300

(a⁶ b^-5)/(a^-2b⁷)

What is a⁸/b¹²?

400

(a³/b²)⁴

What is a¹²/b⁸?

500

(a²b^-4/b²)⁵

What is a¹⁰/b³⁰?

Growth and Decay

100

Joey deposited $50 in a savings account earning 5% interest, compounded annually.
To the nearest cent, how much will he have in 3 years?

What is $57.88?

200

The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)^t where t is the number of years since 1990. What was the population in 1990? By what percent did the population increase by each year?

What is 6191 and 4%?

300

Write a function to describe the situation.
You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%.

What is C = 120 * 0.88^h?

400

A certain type of bacteria grows at a rate proportional to the current population. If a colony of bacteria starts with 500 bacteria and the population doubles every 4 hours, how many bacteria will there be after 12 hours?

3992 bacteria

500

You deposit $1600 in a bank account. Find the balance after 3 years with an interest rate of 2.5% if the interest compounds QUARTERLY.

What is 1,724.21?