Final answer:
The question lacks specific arithmetic expressions to be matched with their simplified forms. However, key concepts for simplifying include adding exponents when multiplying similar bases, representing square roots with fractional powers, and reducing fractions by their greatest common factors.
Step-by-step explanation:
The question seems to involve matching arithmetic expressions with their simplified equivalents. However, the expressions are not properly listed in the question. Nevertheless, let's tackle the conceptual information given in the examples. When simplifying expressions, we employ a variety of arithmetic rules. For instance:
- When multiplying like bases, we add the exponents, as seen with 51 × 51 becoming 52, which is equal to 5.
- The square root of x, denoted √x, can also be represented as x1/2.
- To simplify fractions, we divide both the numerator and the denominator by their greatest common factor.
- Involving divisions and reciprocals, negative exponents imply that the base is in the denominator.
- For division of exponentials, subtract the exponent of the denominator from the exponent of the numerator if the bases are the same.
Always eliminate terms where possible to simplify algebraic expressions, and check to make sure the answer is reasonable.