Evaluate the expression.
$-2 \cdot(-17)$
The problem asks to evaluate the expression \(-2 \cdot (-17)\). This involves the multiplication of two negative numbers. The rule of signs for multiplication states that the product of two negative numbers is always a positive number. Specifically, for any real numbers \(a\) and \(b\), the product of two negatives is given by \((-a) \cdot (-b) = a \cdot b\).
To calculate \(-2 \cdot (-17)\), we identify the absolute values of the two factors, which are 2 and 17. According to the multiplication rule for negative numbers, the result is equivalent to the product of their absolute values: \(-2 \cdot (-17) = 2 \cdot 17\). Performing the multiplication, we find \(2 \times 17 = 34\). Therefore, \(-2 \cdot (-17) = 34\).
In real life, multiplying negative numbers often appears in contexts such as finance or physical measurements. For instance, if you have a debt of \(\$17\) (represented as \(-17\)) and you cancel out 2 such debts (represented as multiplying by \(-2\)), you have effectively gained \(\$34\) in your net worth (\(-2 \times -17 = 34\)). Understanding these operations helps in tracking balances, managing budgets, and interpreting changes in measurements where values can be positive or negative.