Exponential Properties

Vocabulary

100

What do we call numbers that seem to hang in the air and are smaller than typical numbers. For example, the 3 in 2³.

An exponent.

200

What is the name for the large number that is raised to an exponent? For example, the 2 in the expression 2³?

The Base

300

The equation 2³•2⁴=2⁷ displays which property of exponents?

The product of powers property.

Multiplying with Exponents.

400

The equation b⁴÷b³=b displays which property of exponents?

The quotient of a power property.

Dividing with exponents

500

The equation (a³)⁴=2¹² displays which property of exponents?

The power of a power property.

Exponents raised to powers.

Negative Exponents

100

Simplify the given expression:

4^-2•4³

4¹ OR 4

200

Simplify the given expression:

7⁶÷7⁷

7^-1 = 1/7

300

Simplify the given expression:

(-2^-6)^-4

-2²⁴

400

Simplify the following expression:

((n⁴)³ × n²) ÷ n¹⁶

1/n²

500

Simplify the following expression:

(a²)³ × (a⁵)^-² ÷ (a⁴)^-6

a²⁰

More than one variable

100

Simplify the given expression:

x²•m⁴•x⁵

m⁴•x⁷    OR    x⁷•m⁴    OR    m⁴x⁷    OR    x⁷m⁴

200

Simplify the following expression:

(x²y)³

x⁶y³

300

Simplify the following expression:

x⁴y² × x³y⁵

x⁷y⁷

400

Simplify the following expression:

(a²b³)² ÷ a³b

ab⁵

500

Simplify the following expression:

(m³n²)² × m⁴n ÷ (mn²)³

m⁷/n

Word Problems

100

Ashley has a square patch of grass that she needs to determine the area of to create her garden. If one of the sides of the square has a length of b³cm, then what would the area of the square be?

b⁶cm²

200

Mrs. Abigail is trying to teach Mrs. Ford how to divide with exponents. The problem they are looking at says to do 3³ divided by 3⁹ power. Mrs. Ford lost her flip book! What does Mrs. Ford need to do to combine her exponents and what will she get as her final answer?

3-9=-6

3³/3⁹  =  3^-6  =  1/(3⁶)

300

A student was told to simplify the expression (a¹⁴)^-(0.5)

The student gave an incorrect answer of a⁷. Why was the student incorrect, and what answer should they have given?

They did not multiply 14 by -0.5 because they would have gotten -7 instead of 7. The correct answer should have been 1/(a⁷)

400

A certain number, m, is squared and then multiplied by itself raised to an unknown power. The product of both values is m⁸. What would the original expression be before multiplying?

m² • m⁶

500

Emma is designing a video game where players collect power crystals. She created a formula to calculate the strength of a special combination crystal.

The power formula for this crystal is (x²y³)⁴ ÷ (x⁵y)².

Emma wants to simplify this expression to more easily calculate power levels in the game. What is the simplified form of this expression?

y¹⁰/x²

Trivia about Mrs. Abigail

100

What is my favorite color?

Pink

200

How many siblings do I have?

Two, but they're both less cool than I am

300

Where did I go to college?

Carson-Newman University

400

What year did I graduate 8th grade?

2012

500

When I was in 8th grade, I got in trouble while on a field trip and Mr. Chambers had to sit me out with the chaperones for the rest of that day. What did I get in trouble for?

I bought a milkshake at McDonald's when we were only allowed to get soft drinks.