Understanding the Power Rule of Exponents

The video tutorial explains how to simplify expressions using the power rule of exponents. It demonstrates the process through three examples: X^3r^2, (2y^4)^3, and (-3^4)^6. The power rule states that when an exponential term is raised to a power, the exponents are multiplied. The tutorial emphasizes understanding the rule by expanding and verifying the expressions, while also highlighting the importance of leaving expressions in a single base form as instructed.

What is the power rule of exponents?

• When adding like bases, multiply the exponents.

• When raising a power to another power, multiply the exponents.

• When dividing like bases, subtract the exponents.

• When multiplying like bases, add the exponents.

In the expression (x^3)^2, what is the simplified form using the power rule?

• x^9

• x^5

• x^6

• x^8

How can the product rule of exponents be used to verify (x^3)^2?

• By subtracting the exponents of the same base.

• By multiplying the exponents of the same base.

• By dividing the exponents of the same base.

• By adding the exponents of the same base.

What is the result of expanding x^3 in the expression (x^3)^2?

• x * x * x

• x^3 * x^3

• x^6

• x^9

In the expression (2y^4)^3, what is the simplified form using the power rule?

• 2y^10

• 2y^12

• 2y^8

• 2y^7

What is the base in the expression (2y^4)^3?

• 4

• 2

• y

• 2y

In the expression (-3^4)^6, what is the simplified form using the power rule?

• -3^10

• -3^24

• -3^20

• -3^18

What is the exponent in the expression (-3^4)^6 after applying the power rule?

• 18

• 24

• 20

• 10

Why do we not simplify further in the expression (-3^4)^6?

• Because the base is negative.

• Because the directions specify to use a single base.

• Because the exponents are already multiplied.

• Because the expression is already in its simplest form.

What is the key concept when dealing with powers raised to powers?

• Subtract the exponents.

• Divide the exponents.

• Add the exponents.

• Multiply the exponents.