Rational Exponents and Operations

The video tutorial explains how to simplify expressions involving rational exponents by following the same rules used for integer exponents. It provides two examples: the first demonstrates multiplying exponents when a power is raised to another power, and the second shows simplifying expressions inside parentheses and adding exponents. The tutorial also covers converting negative exponents to positive by changing the base's position in a fraction.

What is the primary goal when simplifying expressions with rational exponents?

• To follow the same rules as integer exponents

• To make the base zero

• To convert them into whole numbers

• To eliminate all exponents

In the first example, what operation is performed on the exponents 2/3 and 2/7?

• Addition

• Subtraction

• Multiplication

• Division

What is the result of multiplying the exponents 2/3 and 2/7?

• 8/21

• 2/21

• 6/21

• 4/21

In the second example, what is the first step in simplifying the expression inside the parentheses?

• Subtract the exponents

• Divide the exponents

• Add the exponents

• Multiply the exponents

What is the least common denominator (LCD) used to add the fractions 1/2 and 1/3?

• 6

• 9

• 5

• 3

After finding the common denominator, what is the new exponent inside the parentheses?

• 3/6

• 2/6

• 4/6

• 5/6

What operation is performed on the exponents 5/6 and -2/7 in the second example?

• Addition

• Subtraction

• Multiplication

• Division

What is the simplified exponent after multiplying 5/6 by -2/7?

• -10/21

• -5/21

• -15/21

• -20/21

How can you express X raised to the power of -5/21 with a positive exponent?

• X^5/21

• 1/X^-5/21

• 1/X^5/21

• X^-5/21

What happens to the exponent when the base is moved to the denominator?

• It becomes negative

• It remains unchanged

• It becomes positive

• It becomes zero