Final answer:
The two properties used to write an equivalent expression are division and multiplication. These operations must be applied to all terms in an equation to maintain equality. Exponents and coefficients play roles in altering expressions while preserving their equivalence.
Step-by-step explanation:
The question asks for two properties used to write an equivalent expression. The correct answer is option C) Division and multiplication. These operations, when applied correctly, maintain the equivalence of expressions. For instance, when modifying an equation, if we multiply or divide both sides of the equation by the same non-zero number, the equality holds.
Multiplication or division by the same number must be applied to every term on either side of the equality. If a side contains more than one term, it's crucial to enclose it in small brackets before performing the multiplication or division, ensuring that each term within the bracket is appropriately altered.
The properties of exponents are also significant when dealing with equivalent expressions, especially when raising an entire expression to a power, or when multiplying or dividing terms with exponents. The coefficients in front of variables may change during these operations, but the process is guided by established rules ensuring equivalent expressions result.