Operations with Rational Exponents

This lesson covers operations with rational exponents, including addition, subtraction, multiplication, and division. It explains how to handle fractional exponents and convert them into radical form. The video provides examples of simplifying terms with rational exponents, emphasizing the importance of having the same base for operations. It also discusses the associative and commutative properties of multiplication in the context of exponents.

What must be true for numbers or variables with exponents to be added or subtracted?

• They must have the same coefficient.

• They must be whole numbers.

• They must be positive numbers.

• They must have the same base and dimension.

How can 2 to the 1/3 be expressed using a radical?

• As the square root of 2

• As the cube root of 2

• As the fourth root of 2

• As the fifth root of 2

What does the denominator of a fractional exponent represent in radical notation?

• The base of the radicand

• The index of the radical

• The coefficient of the expression

• The exponent of the radicand

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

• They are subtracted.

• They are divided.

• They remain unchanged.

• They are added.

What is the result of multiplying 9 to the 1/2 by itself three times?

• 81

• 27

• 18

• 9

How can 16 to the 3/4 be simplified?

• As 4

• As 8

• As 16

• As 32

What is the simplified form of 2c to the 3/5 times 2c to the 2/5?

• 8c

• 6c

• 4c

• 2c