Rational Exponents and Their Properties

The video tutorial explains the concept of base and exponent, focusing on expressions with negative rational exponents. It demonstrates how to convert a negative exponent into a positive one and evaluates the expression 32 to the power of negative 3/5. The tutorial also covers how to express a rational exponent as a radical and calculates the final value of the expression.

What is the term used to describe the number 'a' in the expression a^m?

• Exponent

• Base

• Radical

• Index

What is the base in the expression a^m?

• a

• None of the above

• a^m

• m

What is the exponent in the expression a^m?

• None of the above

• a

• a^m

• m

In the expression 32^(-3/5), what is the base?

• 5

• -3/5

• 32

• 3/5

How can an expression with a negative rational exponent be rewritten?

• As a negative number

• As a fraction with a positive exponent

• As a decimal

• As a whole number

What assumption is made when rewriting a negative rational exponent as a positive one?

• The exponent is a whole number

• The base is zero

• The base is a nonzero number

• The exponent is zero

What is the first step in evaluating 32^(-3/5)?

• Divide by 3

• Find the square root

• Rewrite as a positive exponent

• Multiply by 5

What does the denominator of a rational exponent represent when expressed as a radical?

• The power of the radical

• The index of the radical

• The exponent

• The base

In the expression 32^(3/5), what does the numerator represent?

• The base

• The index of the radical

• The exponent

• The power of the value obtained

How can 32^(3/5) be expressed using radicals?

• Square root of 32

• Fifth root of 32, then cubed

• Fourth root of 32, then squared

• Cube root of 32