Simplifying an exponent with a negative rational power

The video tutorial explores the simplification of mathematical expressions involving powers. The teacher introduces a problem and discusses the common mistake of using square roots when cube roots are needed. The tutorial demonstrates how to rewrite numbers to different powers to simplify expressions, emphasizing the importance of matching the power to the denominator. The session concludes with a brief interaction with students, addressing their questions and clarifying concepts.

Describe the process of simplifying the expression 64^(2/3) using the cube root.

How can recognizing that 64 is a square number help in simplifying expressions involving exponents?

What is the significance of rewriting 64 as 8^2 in the context of simplifying expressions?

What is the final simplified answer for the expression 64^(2/3) without using a calculator?

Explain how the denominator affects the power to which a number should be raised when simplifying expressions.