Simplifying Exponential Expressions with the Product Rule

The video tutorial explains the product rule of exponents, which states that when multiplying exponential terms with the same base, you add the exponents. The tutorial provides three examples: multiplying x^2 and x^4, multiplying -2^4 and -2, and multiplying y^4, y^5, and y. Each example demonstrates how to apply the product rule and why it makes sense by expanding the terms. The video emphasizes leaving the product in its exponential form without simplifying further.

What is the product rule of exponents?

• x^a * x^b = x^(a+b)

• x^a * x^b = x^(a*b)

• x^a * x^b = x^(a-b)

• x^a * x^b = x^(a/b)

Using the product rule, what is x^2 * x^4?

• x^2

• x^4

• x^6

• x^8

How many factors of x are there in the expanded form of x^2 * x^4?

• 6

• 5

• 4

• 7

What is the result of -2^4 * -2 using the product rule?

• -2^5

• -2^4

• -2^3

• -2^6

How many factors of -2 are there in the expanded form of -2^4 * -2?

• 5

• 4

• 6

• 3

Why do we leave the product of -2^4 * -2 in the form -2^5?

• Because it is already simplified

• Because the directions say to leave it as a single base

• Because it is a numerical base

• Because it is easier to understand

What is the base in the expression -2^4 * -2?

• 2

• -2

• 4

• -4

What is y^4 * y^5 * y^1 simplified using the product rule?

• y^12

• y^10

• y^11

• y^9

How do you write y as an exponent when it appears alone in a product?

• y^0

• y^1

• y^2

• y^3

What is the sum of the exponents in y^4 * y^5 * y?

• 11

• 8

• 9

• 10