Final answer:
The phrase 'a number decreased by the square of 9' refers to subtracting 81 from a number since 9 squared equals 81. It's an arithmetic operation used in algebra to simplify expressions.
Step-by-step explanation:
The student's question involves arithmetic operations and basic concepts of exponents. A number decreased by the square of 9 refers to taking a certain number and subtracting 81 from it because 9 squared (9²) is equal to 9 x 9, which equals 81. This is an example of combining like terms and simplifying expressions, fundamental skills in algebra.
In algebraic terms, if we let x represent the number, the expression can be written as x - 9², which simplifies to x - 81. This shows how to solve for the unknown value after simplifying an expression, such as reducing the denominator to a perfect square or using the rule of exponents to simplify scientific notation, like expressing 965 as 9.65 × 10².