How to find the derivative of square root and cube root using power rule

The video tutorial explains the use of rational powers and the application of the power rule in mathematical expressions. It covers the process of handling negative powers by converting them to positive and placing them in the denominator. The tutorial concludes with a final simplification of the expression and a brief discussion on presentation preferences.

What is the initial expression involving rational powers discussed in the video?

• X to the 1/3 and 7 * X to the 1/2

• X to the 2/3 and 5 * X to the 1/4

• X to the 1/2 and 6 * X to the 1/3

• X to the 3/4 and 4 * X to the 1/5

What is the result of applying the power rule to the expression 1/2 X to the negative 1/2?

• 1/2 X to the 3/2

• 1/2 X to the 2/3

• 1/2 X to the negative 1/2

• 1/2 X to the 1/2

Why do we need to rewrite expressions with negative exponents in the denominator?

• To make them easier to add

• To convert them into positive exponents

• To change their base

• To simplify multiplication

What is the simplified form of the expression after applying the power rule and rewriting negative exponents?

• 1 / X to the 2/3 - 2 / 2 X to the 1/2

• 2 / X to the 1/2 - 1 / 2 X to the 2/3

• 2 / 2 X to the 1/2 - 1 / X to the 2/3

• 1 / 2 X to the 1/2 - 2 / X to the 2/3

Where is the term '-2' placed in the final expression?

• As an exponent

• In the denominator

• In the numerator

• Outside the fraction