Adding and Subtracting Rational Expressions

The video tutorial covers section 5.2 on properties of rational exponents and radicals. It begins with an introduction to the simplest form of a radical, explaining that no radicands should have a perfect nth power as a factor, contain fractions, or appear in the denominator. The tutorial then discusses the importance of conjugates in eliminating radicals from denominators and introduces like radicals. It further explains various properties of rational exponents, such as the product of a power, power of a power, negative exponents, zero exponents, and quotient of powers. The properties of radicals are also covered, including the product and quotient properties. The video concludes with examples demonstrating how to simplify expressions using these properties.

What is a condition for a radical to be in its simplest form?

• The radicand must be a prime number.

• The radicand must have a perfect nth power as a factor other than one.

• The radicand must be a fraction.

• The radicand must be a whole number.

Which of the following is true about conjugates?

• Conjugates are used to eliminate radicals in the numerator.

• Conjugates are used to multiply radicals.

• Conjugates are used to eliminate radicals in the denominator.

• Conjugates are used to add radicals.

What must be true for two radicals to be considered like radicals?

• They must have the same coefficient.

• They must have the same index and radicand.

• They must have the same base.

• They must have the same exponent.

What is the result of multiplying a^m by a^n?

• a^(m-n)

• a^(m+n)

• a^(m*n)

• a^(m/n)

What does a negative exponent indicate?

• The reciprocal of the base raised to the positive exponent.

• The base raised to the positive exponent.

• The base raised to the zero power.

• The base raised to the negative exponent.

What is the value of any number raised to the zero power?

• Zero

• The number itself

• Undefined

• One

What is the product property of radicals?

• The product of two radicals is the sum of the radicands.

• The product of two radicals is the quotient of the radicands.

• The product of two radicals is the difference of the radicands.

• The product of two radicals is the product of the radicands.

How can you simplify the expression (2 * 3)^3 * (2 * 3)^(-1/3)?

• 3

• 1/3

• 6

• 1/6

What is the simplified form of 10^(1 - (-4/5))?

• 10^(1/5)

• 10^(9/5)

• 10^(4/5)

• 10^(5/9)

What is the sixth root of 25 * 625?

• 5

• 25

• 625

• 125