What is the value of the expression ` a^(3) - 5 + (128)/(16a) ` when a = 2 ?

Options

A. 2
B. 5
C. 7
D. 8

Answer

To find the value of the expression \( a^3 - 5 + \frac{128}{16a} \) when \( a = 2 \), we can follow these steps:

### Step 1: Substitute \( a = 2 \) into the expression
We start with the expression:
\[ a^3 - 5 + \frac{128}{16a} \]
Substituting \( a = 2 \):
\[ 2^3 - 5 + \frac{128}{16 \cdot 2} \]

### Step 2: Calculate \( 2^3 \)
Calculate \( 2^3 \):
\[ 2^3 = 8 \]
So, the expression now becomes:
\[ 8 - 5 + \frac{128}{16 \cdot 2} \]

### Step 3: Calculate \( 16 \cdot 2 \)
Now calculate \( 16 \cdot 2 \):
\[ 16 \cdot 2 = 32 \]
Thus, we have:
\[ 8 - 5 + \frac{128}{32} \]

### Step 4: Calculate \( \frac{128}{32} \)
Now, calculate \( \frac{128}{32} \):
\[ \frac{128}{32} = 4 \]
So the expression simplifies to:
\[ 8 - 5 + 4 \]

### Step 5: Perform the addition and subtraction
Now, we perform the operations:
\[ 8 - 5 = 3 \]
Then add \( 4 \):
\[ 3 + 4 = 7 \]

### Final Result
Thus, the value of the expression when \( a = 2 \) is:
\[ \boxed{7} \]