`32^(2)-x^(3)=8^(3)+13^(2)`

Options

A. 6
B. 8
C. 4
D. 7

Explanation

To solve the equation \( 32^2 - x^3 = 8^3 + 13^2 \), we will follow these steps:

### Step 1: Calculate \( 32^2 \)
First, we need to calculate \( 32^2 \):
\[ 32^2 = 1024 \]

### Step 2: Calculate \( 8^3 \)
Next, we calculate \( 8^3 \):
\[ 8^3 = 8 \times 8 \times 8 = 512 \]

### Step 3: Calculate \( 13^2 \)
Now, we calculate \( 13^2 \):
\[ 13^2 = 169 \]

### Step 4: Add \( 8^3 \) and \( 13^2 \)
Now, we add the results from Step 2 and Step 3:
\[ 8^3 + 13^2 = 512 + 169 = 681 \]

### Step 5: Set up the equation
Now we substitute back into the original equation:
\[ 1024 - x^3 = 681 \]

### Step 6: Isolate \( x^3 \)
To isolate \( x^3 \), we rearrange the equation:
\[ 1024 - 681 = x^3 \]
\[ x^3 = 1024 - 681 \]
\[ x^3 = 343 \]

### Step 7: Find the cube root of \( x^3 \)
Now we find the value of \( x \) by taking the cube root of both sides:
\[ x = \sqrt[3]{343} \]

### Step 8: Simplify the cube root
We can express \( 343 \) as \( 7^3 \):
\[ 343 = 7 \times 7 \times 7 = 7^3 \]
Thus,
\[ x = 7 \]

### Final Answer
The value of \( x \) is \( 7 \).

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