Exponents and Roots Practice Problems

The video tutorial covers the concept of rational exponents, explaining how to convert roots into fraction exponents and vice versa. It demonstrates the conversion of cube roots and other roots into rational exponents, and how to rewrite fraction exponents using radical notation. The tutorial also includes evaluating and simplifying expressions, handling negative exponents, and performing complex operations with exponents and roots.

What is the rational exponent form of the fourth root of a number?

• 1/2

• 1/3

• 1/4

• 1/5

How would you express the cube root of a number using rational exponents?

• 1/4

• 1/3

• 1/5

• 1/2

How do you express the fifth root of a number using rational exponents?

• 1/2

• 1/3

• 1/4

• 1/5

If you have the expression X^2 and you want to apply the cube root, what is the resulting exponent?

• 1/3

• 3/2

• 2/3

• 3/1

What is the process to convert a fractional exponent back into radical notation?

• Multiply the exponent by the root

• Divide the exponent by the root

• Add the exponent to the root

• Use the denominator as the root

How do you evaluate an expression with different bases and exponents?

• Subtract the exponents

• Add the exponents

• Multiply the bases

• Evaluate each separately and then multiply

What is the result of 4^(1/2)?

• 4

• 3

• 2

• 1

What is the cube root of 27?

• 5

• 4

• 2

• 3

What is the result of 4^(1/2) * 27^(2/3)?

• 36

• 24

• 12

• 18

How do you handle a negative exponent in an expression?

• Multiply it by the base

• Add it to the base

• Convert it to a positive by moving the base to the denominator

• Ignore it