Exploring Properties of Exponents

The video tutorial focuses on the properties of exponents, specifically the quotient properties. It begins with an introduction to the concept, followed by examples using both numerical and variable bases. The tutorial then explains the power of a quotient property and how to handle negative exponents using reciprocals. The session concludes with practice problems to reinforce the learned concepts.

What is the result of 3^7 divided by 3^5?

• 3^12

• 3^2

• 3^35

• 3^-2

When dividing powers with the same base, what operation is performed on the exponents?

• Division

• Multiplication

• Subtraction

• Addition

What is the result of x^8 divided by x^6?

• x^-2

• x^14

• x^2

• x^48

What does a negative exponent signify in terms of operations?

• Division

• Multiplication

• Reciprocal

• Addition

How do you simplify (3/2)^2?

• 9/4

• 6/4

• 3/4

• 5/4

What is the result of raising 4/7 to the 5th power?

• 625/2401

• 625/16807

• 1024/2401

• 1024/16807

What is the simplified form of x^7 * y^2 under a seventh root?

• x^(1/7) * y^(2/7)

• x * y^(1/7)

• x^(1/7) * y^(1/7)

• x * y^(2/7)

What is the result of 5^2 divided by 6^2?

• 25/36

• 11

• 1/36

• 30

How do you handle a negative exponent when simplifying expressions?

• Add the exponent to the base

• Take the reciprocal of the base

• Subtract the exponent from the base

• Multiply the base by the exponent

What is the result of applying the power of a quotient property to (3b/a)^4?

• 81b^4/a^3

• 12b^3/a^3

• 12b^4/a^4

• 81b^4/a^4