Evaluate the expression.
$-7^2$
$-7^2$
Evaluate the expression.
$-7^2$
To evaluate the expression \(-7^2\), we must first recognize the order of operations, often abbreviated as PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). In mathematical notation, an expression like \(-x^n\) is evaluated as \(-(x^n)\), which means the exponentiation is performed before the negation. If the intent was to square the negative number itself, parentheses would be used, as in \((-7)^2\).
Following the order of operations, we first perform the exponentiation on the base \(7\):
\[ 7^2 = 7 \times 7 = 49 \]
Next, we apply the negation sign to the result of this exponentiation:
\[ - (7^2) = -49 \]
Thus, the value of the expression is \(-49\).
Understanding the order of operations is crucial in everyday life, especially in fields like finance, engineering, and computer programming. For example, if a program calculates a financial deficit by squaring a loss value, misinterpreting the order of operations could lead to a massive error in the balance sheet. By strictly following mathematical conventions, we ensure accuracy in calculations, whether we are calculating compound interest, scaling dimensions in architecture, or balancing a budget. This simple rule helps prevent misinterpretations of data and keeps complex calculations consistent.