`16^(3//4)` is equal to :

Options

A. `4sqrt(2)`
B. `8`
C. `2sqrt(2)`
D. `16`

Answer

To solve the expression \( 16^{\frac{3}{4}} \), we can follow these steps:

### Step 1: Rewrite the Base
First, we can express 16 as a power of 2. We know that:
\[ 16 = 2^4 \]

### Step 2: Substitute the Base
Now, we can substitute \( 16 \) in the original expression:
\[ 16^{\frac{3}{4}} = (2^4)^{\frac{3}{4}} \]

### Step 3: Apply the Power of a Power Rule
Using the power of a power rule, which states that \( (a^m)^n = a^{m \cdot n} \), we can simplify further:
\[ (2^4)^{\frac{3}{4}} = 2^{4 \cdot \frac{3}{4}} \]

### Step 4: Simplify the Exponent
Now, calculate the exponent:
\[ 4 \cdot \frac{3}{4} = 3 \]
Thus, we have:
\[ 2^{4 \cdot \frac{3}{4}} = 2^3 \]

### Step 5: Calculate the Final Value
Now we can calculate \( 2^3 \):
\[ 2^3 = 8 \]

### Final Answer
Therefore, the value of \( 16^{\frac{3}{4}} \) is:
\[ \boxed{8} \]

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