`(5(8^(1//3)+27^(1//3))^(3))^(1//4)`=

Options

A. 3
B. 6
C. 5
D. 4

Answer

To solve the expression \((5(8^{1/3} + 27^{1/3})^3)^{1/4}\), we can follow these steps:

### Step 1: Simplify the cube roots
First, we simplify \(8^{1/3}\) and \(27^{1/3}\):
- \(8^{1/3} = 2\) (since \(2^3 = 8\))
- \(27^{1/3} = 3\) (since \(3^3 = 27\))

So, we can rewrite the expression as:
\[ (5(2 + 3)^3)^{1/4} \]

### Step 2: Add the values inside the parentheses
Now, we calculate \(2 + 3\):
\[ 2 + 3 = 5 \]

Thus, the expression becomes:
\[ (5(5)^3)^{1/4} \]

### Step 3: Calculate \(5^3\)
Next, we calculate \(5^3\):
\[ 5^3 = 125 \]

Now, we can rewrite the expression as:
\[ (5 \times 125)^{1/4} \]

### Step 4: Multiply the values
Now, we multiply \(5\) and \(125\):
\[ 5 \times 125 = 625 \]

So, the expression now is:
\[ (625)^{1/4} \]

### Step 5: Calculate the fourth root
Finally, we find the fourth root of \(625\):
\[ 625 = 5^4 \quad \text{(since } 5^4 = 625\text{)} \]
Thus,
\[ (625)^{1/4} = 5 \]

### Final Answer
The value of the expression \((5(8^{1/3} + 27^{1/3})^3)^{1/4}\) is:
\[ \boxed{5} \]