Exploring Rational Exponents and Radicals

The video tutorial covers rational exponents and radicals, explaining how rational numbers can be expressed as fractions and how radicals relate to square roots. It demonstrates converting between radical and exponential forms, applying exponent rules, and performing advanced operations with exponents and radicals. The tutorial provides examples of cube roots, higher order roots, and emphasizes understanding the index and exponent in these mathematical expressions.

What is a rational number?

• A number that can be written as a fraction

• A number that cannot be written as a fraction

• A number that is always an integer

• A number that is always a decimal

What is the index in the radical expression √25?

• 2

• 1

• 4

• 3

What is 25 to the 1/2 power?

• 25

• 5

• 2.5

• 12.5

What is the cube root of 729?

• 81

• 27

• 9

• 3

How do you write 36^(1/2) in radical form?

• 36^(1/3)

• 36^(2)

• 36√2

• √36

What is the fifth root of 32?

• 2

• 4

• 8

• 16

How do you write B^(3/2) in radical form?

• B^(2/3)

• B^(3/4)

• B√3

• √B^3

What is the square root of 144 D^4?

• 12 D^4

• 144 D^2

• 144 D^4

• 12 D^2

What is the result of adding a^(2/3) and a^(2/3)?

• a^(1/3)

• a^(5/3)

• a^(4/3)

• a^(2/3)

How do you simplify the expression (B^(1/3) * B^(1/2))?

• B^(1/6)

• B^(2/3)

• B^(1/5)

• B^(5/6)