Understanding (−64)2/3
The expression (−64)2/3 represents a fractional exponent. Understanding how to solve this problem involves recognizing the key concepts of exponents and roots. Here's a breakdown:
Exponents and Roots
 Exponent: An exponent indicates how many times a base number is multiplied by itself. For example, 2³ means 2 * 2 * 2 = 8.
 Root: A root is the inverse operation of an exponent. The nth root of a number is the value that, when multiplied by itself n times, equals the original number. For example, the cube root of 8 (∛8) is 2, because 2 * 2 * 2 = 8.
Fractional Exponents
A fractional exponent like 2/3 combines both exponent and root concepts. The numerator of the fraction indicates the power, and the denominator indicates the root. Therefore, (−64)2/3 means:
 The cube root of (−64) raised to the power of 2.
Solving the Problem

Cube root of (64): The cube root of 64 is 4, because (4) * (4) * (4) = 64.

Squaring the result: (4)² = 16
Therefore, (−64)2/3 = 16.
Key Points to Remember
 Negative bases: When dealing with fractional exponents and negative bases, remember that an odd root of a negative number is negative, while an even root of a negative number is undefined.
 Calculator use: Most calculators have functions for calculating fractional exponents.
 Fractional exponents are often used in advanced mathematical concepts like calculus and algebra.
By understanding the basics of exponents and roots, you can confidently tackle fractional exponents like (−64)2/3 and many other mathematical expressions.