Exploring Rational Exponents and Their Relationship to Radicals

This video tutorial introduces rational exponents and radicals, starting with basic vocabulary such as index, radical, and radicand. It explains how to find roots like cube, fourth, and fifth roots, and connects fractions as exponents with radicals. The tutorial advances to using larger exponents and demonstrates practical examples of calculations, emphasizing the importance of understanding the relationship between roots and exponents.

What is the term for the small number that indicates the root in a radical expression?

• Base

• Radicand

• Index

• Exponent

In the expression 'cube root of 27', what is the value of the cube root?

• 3

• 27

• 9

• 81

What is the fourth root of 1296?

• 7

• 6

• 5

• 4

Which of the following is the fifth root of 1024?

• 2

• 3

• 5

• 4

In the expression 36^(1/2), what does the '1/2' represent?

• Square root

• Cube root

• Fifth root

• Fourth root

What is the cube root of 64?

• 4

• 2

• 3

• 5

How would you express the fourth root of x to the power of 3?

• (x^3)^(1/4)

• (x^(1/4))^3

• (x^4)^(1/3)

• (x^(1/3))^4

What is the fifth root of 32 to the power of 4?

• 64

• 32

• 16

• 8

What is the simplified form of the square root of 36 cubed?

• 36

• 1296

• 7776

• 216

What is the value of 64 to the power of two-thirds?

• 8

• 64

• 16

• 32