Question

1. -4 + 1

\frac{2(-5 - 19)}{}

1. - 10^{2}+4 - 12
2. 40 - 8^{2}+11

Explanation:

1. For the first - expression \(\frac{2(-5 - 19)}{-4 + 1}\):

• Step 1: Simplify the numerator
• First, calculate the value inside the parentheses in the numerator: \(-5-19=-24\). Then, multiply by 2. So, \(2(-5 - 19)=2\times(-24)=-48\).
• Step 2: Simplify the denominator
• Calculate \(-4 + 1=-3\).
• Step 3: Calculate the fraction
• \(\frac{-48}{-3}=16\).

1. For the second - expression \(-10^{2}+4 - 12\):

• Step 1: Calculate the exponent
• According to the order of operations, calculate \(10^{2}=100\). Then, \(-10^{2}=-100\).
• Step 2: Perform addition and subtraction
• \(-100 + 4-12=-100+(4 - 12)=-100-8=-108\).

1. For the third - expression \(40-8^{2}+11\):

• Step 1: Calculate the exponent
• Calculate \(8^{2}=64\).
• Step 2: Perform addition and subtraction
• \(40-64 + 11=(40 + 11)-64=51-64=-13\).

Answer:

The values of the three expressions are 16, - 108, and - 13 respectively.