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Understanding how to evaluate expressions, especially those that involve fractions and exponents, is essential in mathematics. When an evaluation is required, it means determining the value of a mathematical expression. This process involves following the arithmetic and algebraic rules to simplify and solve the expression correctly.

To evaluate the expression \( \left(\frac{2}{3}\right)^2 \), you interpret it as a fraction where both the numerator and the denominator are raised to the power of two. By following the order of operations, known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), you handle the exponent before other operations. This ensures the solution is accurate and follows mathematical conventions.

Squaring a fraction involves raising both the numerator and the denominator to the power of two. In simple terms, you square each part of the fraction separately, which results in a new fraction.

For the fraction \( \frac{2}{3} \), when squaring:

• The numerator becomes \( 2 \times 2 \), which equals \( 4 \).
• The denominator becomes \( 3 \times 3 \), which equals \( 9 \).

By squaring both the top and bottom numbers, you simplify the fraction according to the exponentiation rule for fractions, resulting in \( \frac{4}{9} \). This process maintains the balance of the fraction and accurately reflects its squared value.

Performing operations on the numerator and denominator separately is crucial for accurately solving fraction expressions. Each part of a fraction has its role, and operations may differ based on whether they are performed on the numerator or the denominator.

When dealing with the expression \( \left(\frac{2}{3}\right)^2 \):

• The numerator operation involves finding \( 2^2 \), leading to a value of \( 4 \).
• The denominator operation involves finding \( 3^2 \), leading to a value of \( 9 \).

These separate calculations are then combined to form the fraction \( \frac{4}{9} \). Understanding these operations allows for an easier and more effective approach to handling fractions with exponents.