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Example of Evaluating 2x2y2x^2y

To evaluate the algebraic expression 2x2y2x^2y when x=14x=\frac{1}{4} and y=23y=-\frac{2}{3}, follow the substitution and simplification steps:

Step 1 — Substitute: Replace xx and yy with their fractional values using parentheses to get 2(14)2(23)2\left(\frac{1}{4}\right)^2\left(-\frac{2}{3}\right).

Step 2 — Simplify exponents: According to the order of operations, square the fraction first: (14)2=116\left(\frac{1}{4}\right)^2 = \frac{1}{16}. The expression is now 2(116)(23)2\left(\frac{1}{16}\right)\left(-\frac{2}{3}\right).

Step 3 — Multiply and divide out common factors: Multiply the numerators and denominators to form a single fraction: 21(2)163\frac{2 \cdot 1 \cdot (-2)}{16 \cdot 3}. Write 1616 as 2242 \cdot 2 \cdot 4 to easily divide out the common factors of 22 and 22 from the numerator and denominator.

Step 4 — Simplify: After removing the common factors, 1-1 remains in the numerator and 434 \cdot 3 in the denominator, resulting in 112-\frac{1}{12}.

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Updated 2026-05-02

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