Understanding Rational Exponents and Their Properties

This video tutorial covers rational exponents and their properties, focusing on the product of powers, power of a power, and power of a product properties. It provides examples and exercises to illustrate these concepts, including simplifying expressions and solving mixed problems. The tutorial aims to enhance understanding of how to manipulate and evaluate expressions with rational exponents.

What is the cube root of 125?

• 3

• 6

• 4

• 5

When multiplying like bases, what should you do with the exponents?

• Divide them

• Add them

• Subtract them

• Multiply them

If you have a base raised to a power, and then raised to another power, what operation do you perform on the exponents?

• Subtract them

• Multiply them

• Divide them

• Add them

What is the result of 4^(1/3) * 4^4 all raised to the 6th power?

• 4^2 * 4^4

• 4^4 * 4^2

• 4^3 * 4^2

• 4^2 * 4^3

How do you handle a product raised to a power?

• Add the exponents

• Divide the exponents

• Multiply the exponents

• Distribute the exponent to each term

What is the cube root of 64?

• 3

• 4

• 5

• 2

How do you simplify 2^(4/5) * 2^(1/2) with a common denominator?

• 2^(9/10)

• 2^(7/10)

• 2^(13/10)

• 2^(11/10)

What is the simplified form of 5^(3/4) raised to the 2/3 power?

• 5^(1/4)

• 5^(1/6)

• 5^(1/3)

• 5^(1/2)

What is the result of multiplying the cube root of 16 by the cube root of 4?

• 5

• 4

• 3

• 2

How do you rationalize the denominator of 1/(3√2)?

• Multiply by 3√2

• Multiply by 3

• Multiply by 2

• Multiply by √2