Exploring Properties of Rational Exponents and Radicals

The video tutorial covers the properties of rational exponents and radicals. It begins with an introduction to rational exponents, explaining that they are fractions in the exponent. The tutorial then provides basic examples of multiplying variables and raising powers to powers. Advanced examples are given, including distributing exponents and handling coefficients. The video also covers negative and zero exponents, explaining how to handle them in equations. Finally, the tutorial discusses radicals, including square and cube roots, and provides examples of multiplying and dividing radicals.

What is the result of multiplying variables with the same base?

• You subtract the exponents

• You add the exponents

• You divide the exponents

• You multiply the exponents

If you have a power raised to another power, what operation do you perform on the exponents?

• Divide the exponents

• Multiply the exponents

• Subtract the exponents

• Add the exponents

When distributing an exponent to a product inside parentheses, what should you do?

• Multiply the exponent with each term inside

• Add the exponent to each term inside

• Divide the exponent by each term inside

• Subtract the exponent from each term inside

What is the simplified form of (2x^3/3y^2)^-1?

• 2x^3/3y^2

• 3y^2/2x^3

• 3y^2/2x

• 1/(2x^3/3y^2)

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

• Undefined

• The number itself

• 1

• 0

How do you handle a negative exponent in a fraction?

• Multiply the exponent by -1

• Subtract the exponent from the denominator

• Flip the fraction and change the sign of the exponent

• Add the exponent to the numerator

What is the cube root of 125x^3?

• 125x

• 25x

• 5x

• 5x^3

When multiplying square roots, what can you do with the numbers inside the roots?

• Divide them

• Multiply them

• Subtract them

• Add them

What is the result of dividing square roots?

• Multiply the numbers inside the roots

• Subtract the numbers inside the roots

• Add the numbers inside the roots

• Divide the numbers inside the roots

What is the simplified form of the square root of 144x^2?

• 12x

• 144x^2

• 144x

• 12x^2