How to evaluate a number raised to a negative rational exponent

The video tutorial explains how to solve the problem of 81 raised to the negative 3/4 power. It begins by introducing the problem and discussing the rules for handling negative exponents. The teacher explains the exponent rule x to the m over n equals the n-th root of x to the m power. The video then demonstrates how to apply this rule to the given problem, addressing the confusion around negative exponents. Finally, the teacher simplifies the expression and finds the solution, offering an alternative method for simplification.

What is the rule for converting x to the m over n?

How do you handle a negative exponent in an expression?

Explain how to simplify the expression 1 over 81 to the 3/4.

What is the value of 81 raised to the 3rd power?

What is the result when you take the 4th root of 81 cubed?