Negative Exponents and Their Effects

The video tutorial guides students through categorizing exponential expressions into specific value ranges. It begins with an introduction to the task and encourages students to attempt it independently. The instructor then explains the use of a number line to visualize categories and proceeds to analyze each expression, focusing on the concept of reciprocals and negative exponents. The tutorial concludes with a summary of results and a check of the answers.

What are the three categories used to classify exponential expressions in this lesson?

• Negative, zero, positive

• Less than -1, between -1 and 0, between 0 and 1

• Less than -1, between 0 and 1, greater than 1

• Less than 0, between 0 and 1, greater than 1

What should you think of when you see a negative exponent?

• Multiply by -1

• Square the base

• Take the reciprocal

• Add 1 to the exponent

What is the result of 7 to the negative fourth power?

• A small negative number

• A large negative number

• A small positive number

• A large positive number

How does a negative base raised to an odd exponent behave?

• It becomes zero

• It remains negative

• It becomes undefined

• It becomes positive

What is the result of negative 7 to the third power?

• Less than -1

• Between -1 and 0

• Between 0 and 1

• Greater than 1

What happens when a negative base is raised to an even exponent?

• The result is negative

• The result is positive

• The result is undefined

• The result is zero

What is the result of negative 7 to the negative fourth power?

• Between -1 and 0

• Between 0 and 1

• Less than -1

• Greater than 1

What is the result of negative 7 to the negative fifth power?

• Between -1 and 0

• Between 0 and 1

• Less than -1

• Greater than 1

What is the result of negative 7 to the fifth power?

• Greater than 1

• Less than -1

• Between 0 and 1

• Between -1 and 0

What is the general effect of raising a negative base to an odd exponent?

• The result is positive

• The result is negative

• The result is zero

• The result is undefined