Question

evaluate $(-3)^2 + (-2)^3 \div 2 + 15$.

Explanation:

Step1: Calculate exponents

First, we calculate the values of the exponents. For \((-3)^2\), we know that squaring a negative number gives a positive result, so \((-3)^2 = (-3)\times(-3)=9\). For \((-2)^3\), cubing a negative number gives a negative result, so \((-2)^3 = (-2)\times(-2)\times(-2)= -8\).
So now the expression becomes \(9 + (-8)\div2 + 15\).

Step2: Perform division

Next, we perform the division operation. According to the order of operations (PEMDAS/BODMAS), division comes before addition and subtraction. So we calculate \((-8)\div2=-4\).
Now the expression is \(9+(-4)+15\).

Step3: Perform addition

Now we perform the addition operations from left to right. First, \(9+(-4)=9 - 4 = 5\). Then, \(5 + 15 = 20\).

Answer:

\(20\)