Converting Radicals to Rational Exponents

The video tutorial covers the conversion between radicals and rational exponents. It begins with an introduction to the components of a radical, such as the radical sign, radicand, and index. The tutorial then explains the rules for converting exponential expressions to radicals and vice versa, providing examples for each conversion type. The video concludes with practice problems to reinforce the concepts learned.

What is the term for the number under the radical sign?

• Radical sign

• Exponent

• Index

• Radicand

How do you express 3 raised to the one-half power as a radical?

• Fourth root of 3

• Fifth root of 3

• Square root of 3

• Cube root of 3

In the expression 5 to the two-thirds power, what is the index of the radical?

• 3

• 5

• 2

• 1

How would you write the square root of 6 as an exponential expression?

• 6 to the one-fifth power

• 6 to the one-fourth power

• 6 to the one-half power

• 6 to the one-third power

What is the simplified form of x raised to the three-ninths power?

• x to the one-third power

• x to the one-half power

• x to the one-fourth power

• x to the one-fifth power

Convert 32 raised to the one-fifth power to a radical expression.

• Fifth root of 32

• Fourth root of 32

• Sixth root of 32

• Seventh root of 32

How do you rewrite x raised to the negative four-thirds power as a positive exponent?

• 1 over x to the four-thirds power

• x to the negative one-third power

• x to the four-thirds power

• 1 over x to the negative four-thirds power

Combine the radicals 2y cubed and z to the one-fourth power into one radical expression.

• Seventh root of 2y cubed z

• Sixth root of 2y cubed z

• Fifth root of 2y cubed z

• Fourth root of 2y cubed z

What is the simplified form of the fifth root of 32?

• 2

• 4

• 8

• 16

How do you express negative 32 raised to the four-fifths power as a radical?

• Fifth root of negative 32

• Sixth root of negative 32

• Seventh root of negative 32

• Fourth root of negative 32