Exploring Rational Exponents and Radical Functions

This video tutorial covers rational exponents and radical functions, reviewing properties of exponents, including zero and negative exponents. It explains the product and quotient of powers, properties of radicals, and techniques for simplifying radical expressions. The tutorial also discusses using conjugates to rationalize denominators and handling variable expressions with absolute values. The session concludes with final examples and a summary of key points.

What is the value of any number raised to the power of zero?

• Undefined

• The number itself

• 1

• 0

How do you simplify an integer raised to a negative power?

• Multiply by -1

• Take the reciprocal

• Add 1 to the exponent

• Square the number

What is the result of multiplying 3^2 by 3^4?

• 3^6

• 3^8

• 3^12

• 3^2

How do you handle a negative exponent inside parentheses?

• Add 1 to the exponent

• Square the base

• Move the base to the other side of the fraction bar

• Ignore the negative sign

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

• 4

• 2

• 8

• 16

How do you find the root of a product?

• Multiply the factors and then find the root

• Add the factors and find the root

• Find the root of each factor and then multiply

• Divide the factors and find the root

What is the fourth root of 256?

• 2

• 4

• 8

• 16

When simplifying variable expressions with even roots, what must you include?

• Ignore the root

• Add 1 to the exponent

• Square the result

• Include absolute value

What is the simplified form of the cube root of 24x^3?

• 6x cube root of 4

• 4x cube root of 6

• 3x cube root of 2

• 2x cube root of 3

How do you get rid of a radical in the denominator?

• Square the denominator

• Add the radical to the numerator

• Multiply by the conjugate

• Multiply by the same radical