Rational Exponents and Radicals

This video tutorial explains how to convert between rational exponent form and radical form. It begins with an introduction to the relationship between the two forms, highlighting that the index of the radical is the denominator of the rational exponent, and the exponent is the numerator. The video provides examples of converting from rational exponent form to radical form, such as x^(3/2) to the square root of x cubed, and from radical form to rational exponent form, like the cube root of x squared to x^(2/3). It also covers simplifying rational exponents by reducing fractions.

What is the denominator of the rational exponent when converting the nth root of a to rational exponent form?

• The numerator of the rational exponent

• The exponent of a

• The index of the radical

• The base of the radical

How is x raised to the power of three halves expressed in radical form?

• Square root of x cubed

• Cube root of x squared

• Fourth root of x

• Fifth root of x squared

What is the radical form of b raised to the power of 7/9?

• Seventh root of b to the ninth

• Cube root of b to the ninth

• Ninth root of b to the seventh

• Square root of b to the seventh

In the expression y to the two fifths z to the four fifths, what is the index of the radical in its radical form?

• 5

• 4

• 2

• 9

How is the cube root of x squared expressed in rational exponent form?

• x raised to the power of 1/3

• x raised to the power of 2/3

• x raised to the power of 3/2

• x raised to the power of 2/5

What is the rational exponent form of the 11th root of b to the fifth?

• b raised to the power of 5/11

• b raised to the power of 11/5

• b raised to the power of 5/9

• b raised to the power of 1/5

When converting from radical form to rational exponent form, what does the index of the radical become?

• The base of the rational exponent

• The numerator of the rational exponent

• The denominator of the rational exponent

• The exponent of the base

In the expression y to the 4/6 z to the 2/6, what is the simplified form of the rational exponent for y?

• y to the 3/4

• y to the 4/6

• y to the 2/3

• y to the 1/3

What is the simplified rational exponent form of z to the 2/6?

• z to the 1/3

• z to the 2/3

• z to the 1/2

• z to the 3/2

What is the rational exponent form of the sixth root of y to the fourth z squared?

• y to the 3/4 z to the 1/2

• y to the 2/3 z to the 1/3

• y to the 4/6 z to the 2/6

• y to the 1/3 z to the 2/3