Exponent Laws

Multiplying and Dividing Powers

100

When multiplying powers, which would be the correct way of answering?

 1.(a^r)(a^w)=(a^r+w)

 2.(a^r)(a^w)=(a^rxw)

(a^r)(a^w)=(a^r+w)

200

Write the following equation as 2 powers. Then write it as a single-power

(4x4x4x4x4)÷(4x4x4)

(4⁵)÷(4³)=(4²)

300

Write the following equation as a single power, (3³x3⁴)÷(3²⁷÷3²²)

(3³x3⁴)÷(3²⁷÷3²²)=

(3⁷)÷(3²⁷÷3²²)=

(3⁷)÷(3⁵)=

3²

400

Write this equation as a single power,

(4²x4³)x(4³x4¹)÷(4³x4³)

4³

500

Write this equation as a single power,

(3⁵÷3²)x(3⁸x3⁹)÷(3¹⁶÷3⁷)x(3¹x3²)

3¹⁴

Raising Powers and a Product to a Exponent(s)

100

When raising a product to an exponent, which would be the correct way to solve?

1. (ab)³=(axb)³

2.(ab)³=(a³xb³)

2.(ab)³=(a³xb³)

200

Write this equation as 2 powers.

(3x7)⁶

(3⁶x7⁶)

300

Marie has (2³)² people attending her party. If half her guests leave, how many people will be left?

32 people

400

Write this equation as a single-power

(3x3x3x3x3)²÷(3÷3÷3)³

3¹

500

Write this equation as a single-power

(4x4)⁷x(4x4)³÷(4x4)⁵

4¹⁰

Raising a Quotient to an Exponent

100

When raising a quotient to an exponent, which would be the correct solution?

1. (a/b)²= (a/b²)

2.(a/b)²= (a²/b²)

2.(a/b)²= (a²/b²)

200

Write this equation as a single power,

(4x4)⁶

4¹²

300

Write this equation as a single-power 

(5÷5÷5)⁷

5²¹

400

Solve the equation

(8⁴)÷(4²)

(8⁴)÷(4²)=

(2³)⁴÷(2²)²=

(2⁸)

500

Solve the equation

(6³)÷(3²)

(6³)÷(3²)=

(2³)x(3³)÷(3²)=

(2³)x3=

24

Raising a Quantity to an Exponent of 0

100

Which is the correct answer?

1. a⁰=a

2. a⁰=1

a⁰=1

200

Solve the equation 

(4⁵÷4³)⁰

1

300

Solve the equation, 

(3³÷3²)⁰

1

400

Solve the equation

-(4³x4⁶x4¹)⁰

-1

500

-(3⁵÷3²x3⁸x3⁹÷3¹⁶÷3⁷x3¹x3²)⁰

-1

Exponent Trivia

100

What's a way to remember these exponent laws?

You can practice applying these laws through textbook questions. The more you practice them and how they work the easier it becomes to remember them.

200

What are good ways to deepen and strengthen your understanding of these laws? 

There are plenty of good ways to deepen your understanding of these laws. Things such as practicing textbook questions, playing games based on exponents, like the one right now, listening to songs based on exponents, or even flash cards. 

300

How can you predict the comprehension of these laws to help you in later years of math, (be specific)?

Algebra, exponents, and other math will all build on these laws. If we deeply understand these laws, we can learn the harder math. It will help us to understand further topics and figure things out proactively. 

400

Why do we need to know and understand these laws?

These laws could become the foundation for more difficult math later on. If we deeply understand how to use these laws and how they work, it will become easier to understand harder math later. It's like when you're building something. Without a strong foundation, the whole thing will collapse. We also need to understand these laws so we can pass the test. 

500

Did I get a good grade?

Yes

No

Yes (hopefully)