Rational Exponents and Cube Roots

The video tutorial explains how to evaluate expressions using rational exponents. It begins with an introduction to rational exponents and the process of rewriting radicals as rational exponents. The tutorial then demonstrates how to simplify expressions with negative exponents and apply exponent rules to further simplify expressions. The lesson concludes with a summary of the key points covered.

What is the first step in evaluating expressions using rational exponents?

• Multiply the exponents.

• Add the exponents.

• Rewrite the radical as a rational exponent.

• Convert the expression to a decimal.

What is the purpose of using rational exponents?

• To convert decimals to fractions.

• To avoid using radicals.

• To complicate calculations.

• To simplify expressions.

How can you express a radical in terms of exponents?

• By using a square root.

• By using a fraction.

• By using a logarithm.

• By using a rational exponent.

What is the rational exponent form of the cube root of negative 125?

• (-125)^1/2

• (-125)^2

• (-125)^1/3

• (-125)^3

Which number raised to the third power equals negative 125?

• Negative 6

• Negative 5

• Negative 4

• Negative 3

What is the result of (-5)^3?

• 125

• Negative 125

• Negative 25

• 25

What is the first step in simplifying (-125)^(1/3)?

• Multiply by 3.

• Rewrite as (-5)^3.

• Divide by 3.

• Find the square root.

What is the base when rewriting negative 125 as a power?

• Negative 6

• Negative 5

• Negative 4

• Negative 3

What is the exponent of the base when rewriting (-125) as a power?

• 2

• 4

• 3

• 1

What is the result of multiplying the exponents 3 and 1/3?

• 9

• 1

• 3

• 1/3