Rational Exponents and Radical Expressions

The video tutorial explains how to divide expressions with rational exponents, which are essentially fractional exponents. It begins with an introduction to the concept and then demonstrates the process through two example problems. The first example involves simplifying an expression with a single variable, while the second example includes two variables. The tutorial covers the rules for dividing exponents, finding common denominators, and converting between rational exponents and radicals. It also addresses the importance of not having radicals in the denominator and how to rationalize them.

What is another term for rational exponents?

• Imaginary numbers

• Whole numbers

• Fractional exponents

• Negative exponents

When dividing terms with the same base, what operation is performed on the exponents?

• Subtraction

• Multiplication

• Addition

• Division

What is the common denominator used to simplify the exponents 12 and 2/3?

• 3

• 6

• 12

• 18

What does a sixth root mean in terms of exponents?

• Exponent of 1/3

• Exponent of 1/2

• Exponent of 6

• Exponent of 1/6

Why do we multiply by 5x^(5/6) when rationalizing the expression?

• To simplify the numerator

• To eliminate the radical

• To add more terms

• To change the base

What is the result of multiplying 5 * x^(5/6) by x^(1/6)?

• x^(11/6)

• x^(5/6)

• x^(1)

• x^(6/6)

In the second example, what is the assumed exponent for y in the numerator?

• 2

• 1/2

• 1

• 0

How can the expression x^(3/4) y^(1/2) be rewritten using radicals?

• Fourth root of x times square root of y

• Square root of x times fourth root of y

• Cube root of x times square root of y

• Square root of xy

What is the final simplified form of x^(3/4) y^(1/2) in terms of rational exponents?

• x^(1/2) y^(1/4)

• x^(1/4) y^(1/2)

• x^(1/2) y^(1/2)

• x^(3/4) y^(1/2)

What is the purpose of converting rational exponents to radical form?

• To avoid radicals in the denominator

• To simplify expressions

• To eliminate fractions

• To make calculations easier