Exponents and Rational Exponents Concepts

The video tutorial covers rational exponents, explaining their properties and how to evaluate expressions involving them. It includes practice problems and advanced concepts, emphasizing the importance of understanding exponent rules and simplification techniques.

What is the nth root of a number 'a' when expressed as a rational exponent?

• a to the power of n

• a to the power of 1/n

• n to the power of a

• 1 to the power of a/n

If a base is positive and the denominator of the exponent is even, what is the result?

• Not a real number

• The base itself

• The negative nth root of the base

• The positive nth root of the base

What happens when a negative base is raised to an even denominator?

• The result is positive

• The result is negative

• The result is not real

• The result is zero

For a rational exponent with an odd denominator, what can be said about the result?

• It is not real

• It depends on the base

• It is always negative

• It is always positive

What is the result of 36 raised to the 1/2 power?

• 9

• 12

• 6

• 18

Which rule allows you to add exponents when multiplying like bases?

• Power rule

• Quotient rule

• Product rule

• Negative exponent rule

How do you simplify 27^(1/3) * 27^(5/3) / 27^3?

• 1/27

• 27

• 81

• 1