f) \( -21:(-3)-[4 \cdot(-8)+1]= \)

To solve the expression \( -21:(-3)-[4 \cdot(-8)+1] \), we start with the division and multiplication first. 1. Calculate \( -21 : (-3) = 7 \). 2. Next, evaluate \( 4 \cdot (-8) = -32 \). 3. Now, substitute this value into the bracket: \( -32 + 1 = -31 \). 4. Finally, combine the results: \( 7 - (-31) = 7 + 31 = 38 \). So, the answer is \( 38 \). Let's dive into a brief historical tidbit about mathematical symbols! The division symbol (:) has roots that trace back through history, with various cultures using different representations. The modern division symbol we see now wasn't standardized until the 17th century! If you're tackling math problems rest assured you're not alone. A common mistake is forgetting the order of operations, leading to wrong answers. Always remember to use PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) to guide your calculations. Happy solving!