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Numerical expressions are a way to represent a specific number or value using numbers and mathematical symbols. This could include integers, fractions, decimals, and various mathematical operations like addition, subtraction, and exponentiation. In the original exercise, the expression is

• (-64)^{\frac{3}{3}}

Here, the main operation is an exponentiation, where

• -64 is the base number
• \(\frac{3}{3}\) is the exponent.

To evaluate such expressions correctly, one must understand both the order of operations and how exponents function. These expressions help simplify tasks like computation, algebraic manipulation, and even solving real-world mathematical problems by serving as a shorthand notation.

Simplifying fractions is a fundamental skill in mathematics, where you reduce a fraction to its simplest form. This is done by dividing both the numerator and the denominator by their greatest common divisor (GCD). In the exercise, we have the exponent \(\frac{3}{3}\).

• Here, both 3 and 3 share a GCD of 3.

Thus, dividing both by 3 gives us 1, simplifying the fraction to 1. This simplification not only makes calculations easier but also often reveals direct relationships in expressions, as seen in the transformation from \[(-64)^{\frac{3}{3}}\] to \[(-64)^1\]. By understanding this concept, one can make complex problems more manageable and avoid unnecessary computation steps.

Evaluating expressions involves calculating the final value of an algebraic or numerical expression. This requires following the correct sequence of operations. In our example, after simplifying the fraction to 1, the expression becomes \((-64)^1\). The rule to remember here is that any number to the power of 1 is the number itself.

• Thus, \((-64)^1\) simply equals -64.

Evaluating expressions expertly can immensely aid in more elaborate topics like calculus or algebra. It involves a solid grasp of basic arithmetic operations, understanding of exponents, and the patience to perform calculations step by step. Mastering these basics allows students to approach new problems with confidence, knowing that they can handle various mathematical challenges.