Exponent Properties and Simplification

The video tutorial explains how to simplify the expression 4a squared b raised to the third power by applying the property of exponents. It begins with an introduction to the problem, followed by an explanation of the exponent property using a simple example. The property states that when a product is raised to a power, each factor can be raised to that power individually. The tutorial then applies this property to the given problem, demonstrating the step-by-step simplification process. The final result is 64a to the sixth power b to the third power.

What is the initial expression that needs to be simplified?

• 4a squared b squared

• 4a cubed b raised to the third power

• 4a squared b raised to the third power

• 4a squared b raised to the second power

According to the property of exponents, (a * b)^n is equal to:

• a * b^n

• a^n * b^n

• a^n * b

• a^n + b^n

In the example given, what is the result of (a * b)^3?

• a^3 + b^3

• a * b^3

• a^2 * b^2

• a^3 * b^3

What property allows us to rearrange the terms in a multiplication?

• Identity property

• Associative property

• Distributive property

• Commutative property

When applying the exponent property to 4a squared b, what is the first step?

• Multiply all terms by 3

• Raise each component to the third power

• Add 3 to each exponent

• Divide each component by 3

What is 4 raised to the third power?

• 64

• 32

• 16

• 128

How do you simplify a squared raised to the third power?

• a^3

• a^5

• a^6

• a^9

What is the result of multiplying 16 by 4?

• 80

• 64

• 48

• 32

What is the final simplified form of the expression?

• 64 a^6 b^3

• 64 a^3 b^6

• 64 a^5 b^3

• 64 a^6 b^2

Which color was used to highlight the third power in the explanation?

• Magenta

• Yellow

• Green

• Blue