Simplify the expression below using order of operations.

Question

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: \[ \boxed{2} \]