Exploring Properties of Exponents

This video lesson by Kirk Weiler covers unit seven, lesson two on more properties of exponents. It begins with a review of basic exponent properties, focusing on multiplying expressions with the same base. The lesson progresses to expanding and simplifying expressions using exponent rules, including the product and quotient rules. The use of calculators for exponentiation and handling negative bases is also discussed. The power of a power rule is explained, followed by simplifying complex expressions using multiple exponent rules. The lesson concludes with a summary of the exponent properties covered.

What happens when you multiply two expressions with the same base?

• You add the exponents

• You subtract the exponents

• None of the above

• You divide the exponents

What is the result of (x^5) * (x^3)?

• x^2

• x^8

• x^15

• x^1

How do you simplify a product raised to an exponent, such as (ab)^n?

• a^n / b^n

• a^n * b^n

• a^n - b^n

• a^n + b^n

What is the simplified form of (x/y)^3?

• x^3 + y^3

• x^3 - y^3

• x^3 * y^3

• x^3 / y^3

If you have a product inside an exponent, like (2x)^3, how do you simplify it?

• 6x

• 2^3 * x^3

• 2^3 + x^3

• 8x^3

What is the correct simplification of (5x)^2?

• 5x^4

• 25x^4

• 10x

• 25x^2

What is the result of raising a negative number to an even power?

• A positive number

• A negative number

• The base number

• Zero

How do you handle a negative base raised to an odd power, like (-2)^5?

• 2

• Zero

• Negative 32

• Positive 32

What does (x^a)^b simplify to?

• x^(a/b)

• x^(a+b)

• x^(a-b)

• x^(a*b)

What is the result of (y^4)^11?

• y^7

• y^15

• y^22

• y^44