Negative Exponents and Radical Expressions

The video tutorial explains how to simplify expressions with exponents. It covers the process of using exponent rules to simplify expressions with negative exponents, convert them to positive exponents, and finally express them in radical form. The tutorial emphasizes the importance of understanding exponent rules, such as multiplying exponents when raising a power to a power, and converting negative exponents to positive by moving them across the fraction bar. The video concludes with expressing the simplified expression in radical form, highlighting the relationship between rational exponents and radicals.

What is the initial task given in the problem regarding the expression with exponents?

• To integrate the expression

• To solve an equation

• To simplify using negative exponents

• To find the derivative

Which rule is applied to simplify the expression with negative exponents?

• Addition of exponents

• Subtraction of exponents

• Multiplication of exponents

• Division of exponents

What is the simplified expression with negative exponents for X raised to the power of -2/3, raised to the power of 2/5?

• X raised to the power of -4/15

• X raised to the power of 4/15

• X raised to the power of -2/5

• X raised to the power of 2/3

How do you convert a negative exponent to a positive exponent?

• By multiplying the exponent by -1

• By adding 1 to the exponent

• By subtracting 1 from the exponent

• By moving the base to the denominator

What is the expression with positive exponents for X raised to the power of -4/15?

• 1 divided by X raised to the power of 4/15

• X raised to the power of -4/15

• X raised to the power of 4/15

• 1 divided by X raised to the power of -4/15

What does the denominator in a rational exponent represent in radical form?

• The index of the radical

• The base of the radical

• The exponent of the radical

• The coefficient of the radical

In the expression 1 divided by X raised to the power of 4/15, what is the index of the radical?

• X

• 15

• 4

• 1

What is the radicand in the expression 1 divided by the 15th root of X raised to the fourth power?

• 4

• X

• 15

• X to the fourth

How can the exponent of four be expressed in the radical form of the expression?

• Inside the radical

• As a base

• Outside the radical

• As a coefficient

Which of the following expressions are equivalent in radical form?

• 1 divided by the 15th root of X raised to the fourth power and X raised to the power of 4/15

• 1 divided by the 15th root of X raised to the fourth power and 1 divided by X raised to the power of 4/15

• X raised to the power of 4/15 and X raised to the power of -4/15

• 1 divided by X raised to the power of 4/15 and X raised to the power of 4/15