Question

Simplify the expression below using order of operations.
start fraction, minus, 1, plus, left parenthesis, minus, 3, right parenthesis, cubed, divided by, 8, to the power 1 , plus, left parenthesis, minus, 1, right parenthesis, end fraction, divided by, start fraction, 10, plus, left parenthesis, minus, 8, right parenthesis, divided by, 4, plus, left parenthesis, minus, 5, right parenthesis, end fraction
8
1
+(−1)
−1+(−3)
3

​
÷
4+(−5)
10+(−8)
​

Answer 1

To simplify the expression step-by-step, we will follow the order of operations (PEMDAS/BODMAS).

The expression is structured as follows:

\[
\frac{-1 + (-3)^3}{8^1 + (-1)} \div \frac{10 + (-8)}{4 + (-5)}
\]

### Step 1: Calculate the individual components

#### Numerator of the first fraction
1. Calculate \((-3)^3\):
\[
(-3)^3 = -27
\]
2. Now evaluate the entire numerator:
\[
-1 + (-27) = -1 - 27 = -28
\]

#### Denominator of the first fraction
1. Calculate \(8^1 + (-1)\):
\[
8^1 = 8
\]
\[
8 + (-1) = 8 - 1 = 7
\]

So the first fraction becomes:
\[
\frac{-28}{7} = -4
\]

### Step 2: Calculate the second fraction

#### Numerator of the second fraction
1. Calculate \(10 + (-8)\):
\[
10 - 8 = 2
\]

#### Denominator of the second fraction
1. Calculate \(4 + (-5)\):
\[
4 - 5 = -1
\]

So the second fraction becomes:
\[
\frac{2}{-1} = -2
\]

### Step 3: Now we have

The overall expression now simplifies to:
\[
-4 \div (-2)
\]

### Step 4: Perform the division
1. Calculate \(-4 \div (-2)\):
\[
-4 \div -2 = 2
\]

### Final Result
The simplified expression is:
\[
\boxed{2}
\]