Exponents and Their Properties

This video tutorial explains how to simplify expressions using the power of a product rule and the power rule of exponents. It provides multiple examples, demonstrating how to apply these rules to expressions with different bases, including negative bases and negative exponents. The tutorial emphasizes the importance of multiplying exponents when dealing with powers raised to powers and concludes with a simplified expression for each example.

What is the power of a product rule of exponents?

• (a^m)^n = a^(m*n)

• a^m / a^n = a^(m-n)

• (a * b)^n = a^n * b^n

• a^m * a^n = a^(m+n)

Tags

CCSS.8.EE.A.1

What is the power rule of exponents?

• (a * b)^n = a^n * b^n

• a^m * a^n = a^(m+n)

• a^m / a^n = a^(m-n)

• (a^m)^n = a^(m*n)

Tags

CCSS.8.EE.A.1

What is the result of multiplying exponents in (a^m)^n?

• a^(m*n)

• a^(m+n)

• a^(m-n)

• a^(m/n)

Tags

CCSS.8.EE.A.1

How do you simplify (xy^3)^2 using the power of a product rule?

• x^3y^2

• x^2y^3

• x^2y^6

• x^6y^2

Tags

CCSS.8.EE.A.1

What is the result of applying the power rule to (3^a z)^6?

• 3^(a+6) z^6

• 3^a z^6

• 3^(6a) z^6

• 3^(a*6) z^6

Tags

CCSS.8.EE.A.1

What is the simplified form of (3^a z)^6?

• 3^(a*6) z^6

• 3^a z^6

• 3^(a+6) z^6

• 3^(6a) z^6

Tags

CCSS.6.EE.A.1

When simplifying (-4b^5)^2, what is the result of squaring -4?

• -8

• -16

• 8

• 16

What is the simplified form of (-2p)^4?

• 1/16p^2

• -16p^4

• 16p^4

• 1/16p^4

Tags

CCSS.8.EE.A.1

How do you handle negative exponents in an expression?

• Leave them as they are

• Multiply them by the base

• Convert them to positive exponents by taking the reciprocal

• Add them to the base

Tags

CCSS.6.EE.A.1

What is the simplified form of a^(-12) b^8?

• b^8 a^12

• a^(-12) b^8

• a^12 / b^8

• b^8 / a^12

Tags

CCSS.6.EE.A.1