Evaluate:
$(-3)^3-2+8 \div(-8)$
The objective is to evaluate the arithmetic expression \((-3)^3 - 2 + 8 \div (-8)\) by adhering to the order of operations, often referred to as PEMDAS or BODMAS. This rule states that we should perform operations in the following order: Parentheses, Exponents, Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right). We have an exponent, a division, a subtraction, and an addition to handle.
First, we compute the exponentiation: \((-3)^3\). This means multiplying -3 by itself three times:
\[(-3) \times (-3) \times (-3) = 9 \times (-3) = -27.\]
So, the expression becomes \(-27 - 2 + 8 \div (-8)\).
Next, we perform the division according to the order of operations: \(8 \div (-8)\). Dividing 8 by -8 yields:
\[8 \div (-8) = -1.\]
Substituting this value back into our expression gives us:
\[-27 - 2 + (-1).\]
Finally, we perform the addition and subtraction from left to right:
\[-27 - 2 = -29.\]
\[-29 + (-1) = -29 - 1 = -30.\]
Thus, the final result is \(-30\).
Understanding the order of operations is crucial for financial calculations or coding. For instance, if you are tracking your bank balance and you have a base amount, some withdrawals, and a final adjustment, calculating them in the correct order ensures your balance is accurate. If you calculate \(-27 - 2 + 8 \div -8\) incorrectly by just reading left to right without applying the rules, you might get a wrong answer, which in finance would lead to an incorrect account statement. Mastering this ensures your personal accounting remains precise and reliable.