Exponents and Exponential Functions Review

Exponent Properties

100

What is anything to the 0 power?

1!

200

Simplify:

 9y⁴j⁴y^-9

(9j²)/(y⁵)

300

Simplify:

 (a³/m)^-4

(m⁴)/a¹²

400

Simplify:

 (-3q^-1)(3q²)

9q

500

Simplify: 

2y^-9h²(2y⁰h^-4)^-6

(h²⁶)/(32y⁹)

Scientific Notation

100

Convert to standard form:

76 x 10^-9

.000000076

200

The speed of light in a vacuum is about 186,300 mi/s. Use Scientific Notation to express how far light travels in one second.

1.863 x 10⁵

300

Convert 9.55 x 10⁷ to standard form

95,500,000

400

Convert 4.053 x 10^-3 to standard form. 

0.004053

500

In 2000, the total amount of glass recycled in the US was 2.7 million tons. The population of the US in 2000 was 281.4 million people. On average, about how many tons of glass were recycled per person?

9.59 x 10^-3

Exponential Functions

100

Growth or decay?

y = 6(1/3^x)

decay

200

What is the y-intercept:

y = 1/3(2/5^x)

1/3

300

What is the general form of an exponential function?

y = ab^x

400

What is the growth/decay rate?

y=2(3^x)

500

Write an exponential function of the form y = ab^x that goes through (0, 5) and (1, 20)

y = 5(4^x)

Exponent Laws

100

If you multiply two exponents with the same base, what do the exponents do?

ADD!

200

What is the power rule for exponents?

The exponent outside of the parentheses distributes to everything inside!!!! (exponents multiply)

300

Write an expression with exponents that will simplify to 1. 

Answers vary. 

Anything to the 0 power!

400

If you divide two exponents with the same base, the exponents.....

SUBTRACT

500

Explain what a negative exponent does. Give an example. 

Flips the position of the exponent. 

For example - x^-2 = 1/x²