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)

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)

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

• a^(m*n)

• a^(m+n)

• a^(m-n)

• a^(m/n)

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

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

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

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

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

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