Exploring Properties of Rational Exponents

The video tutorial covers the application of rational exponents, starting with basic rules and moving to more complex operations like negative exponents and the quotient rule. It transitions into radicals, explaining their properties and simplification techniques. The tutorial includes examples and practice problems to reinforce learning.

What is the result of 5^(1/2) * 5^(3/2)?

• 1

• 5

• 25

• 125

How do you simplify (3^(5/2))^2?

• 3^5

• 3^10

• 3^7

• 3^2

What happens to a negative exponent in the numerator of a fraction?

• It stays in the numerator

• It moves to the denominator

• It becomes positive

• It is subtracted from the base

What is the cube root of 27?

• 4

• 5

• 3

• 2

How do you combine like terms with the same variable and exponent?

• Divide the coefficients

• Add the coefficients

• Multiply the coefficients

• Subtract the coefficients

What is the simplest form of the third root of 135?

• 5 * third root of 5

• 3 * third root of 3

• 5 * third root of 3

• 3 * third root of 5

How do you simplify the fourth root of 16?

• 2

• 4

• 8

• 16

What is the fifth root of 32?

• 8

• 4

• 2

• 16

How do you simplify (4x^(4/5))^2?

• 16x^(4/5)

• 4x^(4/5)

• 16x^(8/5)

• 4x^(8/5)

What is the result of combining -3 fourth root of 2 and -3 fourth root of 2?

• -6 fourth root of 4

• -3 fourth root of 2

• -3 fourth root of 4

• -6 fourth root of 2