Understanding Rational Exponents and Radicals

The video tutorial explains how to express radical expressions using rational exponents and vice versa. It covers the conversion of the nth root of x to x raised to the power of 1/n and provides examples, such as the cube root of 4 and the fourth root of 2xy^3. The tutorial also demonstrates converting expressions with rational exponents back to radicals, emphasizing the importance of understanding the relationship between the index and the exponent.

What is the rational exponent form of the square root of x?

• x^(2/3)

• x^(1/2)

• x^2

• x^(1/3)

If the nth root of x is expressed as a rational exponent, what does the denominator represent?

• The index of the radical

• The base of the exponent

• The coefficient of x

• The exponent on x

How would you express the cube root of 4 using rational exponents?

• 4^(1/3)

• 4^(2/3)

• 4^(3/2)

• 4^(1/2)

In the expression 3 times the fourth root of 2xy^3, what is the rational exponent of y?

• 2/3

• 1/3

• 3/4

• 1/4

What is the rational exponent form of the expression 2 raised to the power of one fourth?

• 2^(1/4)

• 2^(1/3)

• 2^(3/4)

• 2^(1/2)

What is the rational exponent form of the fourth root of 3x^2?

• (3x^2)^(3/4)

• (3x^2)^(1/2)

• (3x^2)^(2/3)

• (3x^2)^(1/4)

When converting 2x^(1/2) to a radical expression, what is the correct form?

• x√2

• 2x^2

• √2x

• 2√x

In the expression 3x^2 raised to the one-fourth power, what does the one-fourth exponent indicate?

• The fifth root

• The fourth root

• The square root

• The cube root

In the expression 2x^(1/2), what does the numerator of the exponent indicate?

• The coefficient of x

• The exponent on x

• The base of the exponent

• The index of the radical