Exploring Properties of Rational Exponents and Radicals

The video tutorial covers Chapter 5, Section 2, focusing on the properties of rational exponents and radicals. It begins with a review of exponent rules, including product of powers, power of a power, negative exponents, zero exponent, and quotient powers. The tutorial then applies these rules to fractional exponents, providing examples and solutions. The latter part of the video explores properties of radicals, such as the product and quotient properties, and demonstrates how to simplify radical expressions.

What is the rule for the product of powers?

• Divide the exponents

• Subtract the exponents

• Add the exponents

• Multiply the exponents

How do you handle a negative exponent?

• Multiply the base by -1

• Move the base to the opposite part of the fraction

• Subtract 1 from the exponent

• Add 1 to the exponent

What does any number to the power of zero equal?

• One

• The number itself

• Zero

• Negative one

How do you combine exponents when dividing with the same base?

• Add the exponents

• Subtract the exponents

• Multiply the exponents

• Divide the exponents

What is the result of 7^(1/4) * 7^(1/2)?

• 7^(3/2)

• 7^(1/6)

• 7^(1/8)

• 7^(3/4)

How do you distribute an exponent over a product inside parentheses?

• Distribute the exponent to each term inside

• Multiply the exponents

• Subtract the exponents

• Add the exponents

What is the product property of radicals?

• You can multiply the radicals

• You can separate the product inside the radical into two radicals

• You can subtract the radicals

• You can add the radicals

How do you simplify the fourth root of 80 divided by 5?

• Fourth root of 85

• Fourth root of 16

• Fourth root of 20

• Fourth root of 75

What must be done to a radical in the denominator to simplify it?

• Add 1 to the radical

• Multiply the radical by itself

• Subtract 1 from the radical

• Divide the radical by itself

What is the simplified form of (5 + √3) / (5 - √3)?

• (5 + √3) / 25

• (5 - √3) / 25

• (5 + √3) / 22

• (5 - √3) / 22