Understanding Exponents and Radical Expressions

The video tutorial explains how to simplify an expression with exponents and convert it to radical form. It starts by introducing the problem of simplifying x raised to the 3/4 power, then raised to the 2/11 power. The tutorial applies the exponent multiplication rule, simplifies the expression to x raised to the 3/22 power, and demonstrates how to input this into a computer. Finally, it explains how to convert the simplified expression into radical form, highlighting the roles of the numerator and denominator in determining the exponent and index of the radical.

What is the initial expression given in the problem?

• X raised to the 3/4 power raised to the 2/11 power

• X raised to the 2/3 power raised to the 4/11 power

• X raised to the 11/2 power raised to the 3/4 power

• X raised to the 4/3 power raised to the 11/2 power

What rule is applied when a power is raised to another power?

• Multiply the exponents

• Subtract the exponents

• Divide the exponents

• Add the exponents

What is the simplified exponent after applying the exponent rule?

• 3/44

• 3/22

• 6/44

• 6/22

How do you type the simplified expression with positive exponents into a computer?

• X^22/3

• X^3/22

• X^(3/22)

• X^(22/3)

What does the denominator of a rational exponent indicate in radical form?

• The exponent of the radicand

• The index of the radical

• The coefficient of the radicand

• The base of the radical

What is the index of the radical for the expression X^(3/22)?

• 11

• 6

• 3

• 22

What is the radicand in the expression X^(3/22) when written in radical form?

• X raised to the 6th power

• X raised to the 22nd power

• X raised to the 3rd power

• X raised to the 11th power

How can the exponent be expressed in the radical form of X^(3/22)?

• Neither inside nor outside the radical

• Both inside and outside the radical

• Outside the radical only

• Inside the radical only

What are the two equivalent expressions for X^(3/22) in radical form?

• 11th root of X^3 and X^3 inside the 11th root

• 22nd root of X^3 and X^3 inside the 22nd root

• 22nd root of X^2 and X^2 inside the 22nd root

• 11th root of X^2 and X^2 inside the 11th root