Exploring Rational Exponents and Radicals

This video tutorial provides a comprehensive explanation of rational exponents, starting with an introduction to the concept and the basic rules of exponents. It explains how rational exponents are expressed as fractional exponents, where the numerator is the power and the denominator is the index. The video includes several examples to illustrate the conversion between radical and exponential forms, and demonstrates the simplification of complex expressions using power rules. It also covers solving equations involving rational exponents, providing a step-by-step approach. The tutorial concludes with a recap of the key points and encourages viewers to practice further.

What is a rational exponent?

• An exponent that is a whole number

• An exponent that is zero

• An exponent that is a fraction

• An exponent that is negative

In a rational exponent, what does the numerator represent?

• The base

• The power

• The index

• The root

How can the cube root of 27 be written as a rational exponent?

• 27^1/2

• 27^3

• 27^2/3

• 27^1/3

Convert the cube root of x to the fifth power into exponential form.

• x^1/3

• x^3/5

• x^5

• x^5/3

What is the sixth root of n in exponential form?

• n^1/6

• n^6

• n^1/2

• n^1/3

How do you write x to the 5/3 in radical form?

• x^(5/3)

• √(x^5)

• ³√(x^5)

• x^(3/5)

Simplify the expression (x^2/5)^3 using the power rule.

• x^5/6

• x^3/2

• x^6/5

• x^2/15

What does the power rule state?

• A power to a power you add

• A power to a power you divide

• A power to a power you multiply

• A power to a power you subtract

What is the result of 125x^(1/3) = 5 after solving for x?

• x = 5

• x = 1

• x = 25

• x = 125

What is the first step in solving the equation 125x^(1/3) = 5?

• Subtract 5 from both sides

• Cube both sides

• Multiply both sides by 3

• Divide both sides by 125