Understanding Rational Exponents and Radical Forms

The video tutorial explains how to evaluate expressions with rational exponents by converting them into radical form. It covers the process of identifying the base, radicand, index, and exponent. Examples include simplifying expressions like 9 raised to 1/2, 27 raised to 2/3, and handling negative bases. The tutorial also demonstrates converting negative exponents to positive by moving the base to the denominator.

What does the denominator of a rational exponent indicate when converting to radical form?

• The exponent inside the radical

• The index of the radical

• The base of the radical

• The radicand of the radical

When simplifying 9 raised to the power of 1/2, what is the result?

• 4

• 3

• 2

• 1

What type of root is used when simplifying 27 raised to the 2/3 power?

• Fifth root

• Square root

• Fourth root

• Cube root

What is the simplified result of 27 raised to the 2/3 power?

• 9

• 6

• 12

• 15

How should -4 raised to the 1/2 power be interpreted?

• As the negative square root of 4

• As the negative cube root of 4

• As the square root of -4

• As the cube root of -4

What is the result of -4 raised to the 1/2 power?

• -3

• -2

• -4

• -1

How can you rewrite an expression with a negative exponent to make it positive?

• Move the base to the numerator

• Move the base to the denominator

• Multiply by the base

• Divide by the base

What is the simplified form of 1/16 raised to the power of 3/2?

• 1/8

• 1/16

• 1/64

• 1/32

What is the radicand when converting 1/16 raised to the power of 3/2 into radical form?

• 4

• 16

• 1

• 8

What is the cube of the square root of 16?

• 16

• 64

• 8

• 32