find the value of the expression `(64x^(2) + 81y^(2) + 144 xy)` when x = 11 and `y = (4)/(3)`

Answer

To find the value of the expression \(64x^2 + 81y^2 + 144xy\) when \(x = 11\) and \(y = \frac{4}{3}\), we will follow these steps:

### Step 1: Substitute the values of \(x\) and \(y\) into the expression.
We start with the expression:
\[ 64x^2 + 81y^2 + 144xy \]
Substituting \(x = 11\) and \(y = \frac{4}{3}\):
\[ 64(11)^2 + 81\left(\frac{4}{3}\right)^2 + 144(11)\left(\frac{4}{3}\right) \]

### Step 2: Calculate \(x^2\) and \(y^2\).
First, calculate \(11^2\):
\[ 11^2 = 121 \]
Next, calculate \(\left(\frac{4}{3}\right)^2\):
\[ \left(\frac{4}{3}\right)^2 = \frac{16}{9} \]

### Step 3: Substitute the squared values back into the expression.
Now substitute these squared values back into the expression:
\[ 64(121) + 81\left(\frac{16}{9}\right) + 144(11)\left(\frac{4}{3}\right) \]

### Step 4: Calculate each term separately.
1. Calculate \(64 \times 121\):
\[ 64 \times 121 = 7744 \]
2. Calculate \(81 \times \frac{16}{9}\):
\[ 81 \times \frac{16}{9} = 9 \times 16 = 144 \]
3. Calculate \(144 \times 11 \times \frac{4}{3}\):
\[ 144 \times 11 = 1584 \]
\[ 1584 \times \frac{4}{3} = 1056 \]

### Step 5: Add all the calculated values together.
Now, add all the terms:
\[ 7744 + 144 + 1056 \]
Calculating this step-by-step:
\[ 7744 + 144 = 7888 \]
\[ 7888 + 1056 = 8944 \]

### Final Answer:
The value of the expression \(64x^2 + 81y^2 + 144xy\) when \(x = 11\) and \(y = \frac{4}{3}\) is:
\[ \boxed{8944} \]