Key Concepts in Algebraic Expressions

Coefficient: Refers to a numerical factor multiplied by a variable in an expression.
Zero Exponent Rule: Any non-zero number raised to the power of zero equals one (x^0 = 1).
Negative Exponent Rule: A base with a negative exponent represents its reciprocal raised to the positive of that exponent (x^-n = 1/x^n).

Product of Powers Property: When multiplying like bases, add the exponents (a^m * a^n = a^(m+n)).
Power of a Power Property: When raising a power to another power, multiply the exponents ( (a^m)^n = a^(m*n) ).
Quotient of Powers Property: When dividing like bases, subtract the exponents (a^m / a^n = a^(m-n)).

Monomial: An expression consisting of a single term, which can be a number, a variable, or a product of both.
Algebraic Expression: A structure combining numbers, variables, and at least one mathematical operation.
Constant: A specific numerical value that does not change or vary in expression.

Distributive Property: A method to simplify expressions with parentheses by multiplying each term inside the parentheses by the factor outside (e.g., a(b + c) = ab + ac).
Like Terms: Terms that share the same variables raised to the same powers, allowing them to be combined or simplified.
Simplest Form: Refers to an expression free from like terms and parentheses, representing the most reduced version.
Simplify: The process of executing all possible operations within an expression, including combining like terms.
Terms: Constituent elements of an expression, which can be numbers, variables, or combinations thereof.
Variable: Represents an unknown quantity, typically denoted by letters in algebraic expressions.