`(270)/(?)=19xx2-2^(3)`

Options

A. 9
B. 5
C. 6
D. 7

Explanation

To solve the equation \(\frac{270}{?} = 19xx2 - 2^3\), we will follow these steps:

### Step 1: Simplify the right side of the equation
First, we need to interpret \(19xx2\). Assuming \(xx\) represents the digits \(82\), we rewrite it as \(1982\). Now we have:

\[ \frac{270}{?} = 1982 - 2^3 \]

### Step 2: Calculate \(2^3\)
Next, we calculate \(2^3\):

\[ 2^3 = 8 \]

### Step 3: Substitute \(2^3\) back into the equation
Now, substitute \(8\) back into the equation:

\[ \frac{270}{?} = 1982 - 8 \]

### Step 4: Perform the subtraction
Now, we perform the subtraction:

\[ 1982 - 8 = 1974 \]

### Step 5: Rewrite the equation
Now our equation looks like this:

\[ \frac{270}{?} = 1974 \]

### Step 6: Cross-multiply to solve for \(?\)
To find \(?\), we cross-multiply:

\[ 270 = 1974 \times ? \]

### Step 7: Isolate \(?\)
Now, isolate \(?\):

\[ ? = \frac{270}{1974} \]

### Step 8: Simplify the fraction
Now we simplify \(\frac{270}{1974}\). We can divide both the numerator and the denominator by their greatest common divisor (GCD).

Calculating the GCD, we find that both numbers can be divided by 6:

\[ \frac{270 \div 6}{1974 \div 6} = \frac{45}{329} \]

### Final Answer
Thus, the value of \(?\) is:

\[ ? = \frac{45}{329} \]

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