The value of `(256)^(0.16)xx(256)^(0.09)` is :

Options

A. `256.25`
B. `64`
C. `16`
D. `4`

Answer

To solve the expression \((256)^{0.16} \times (256)^{0.09}\), we can follow these steps:

### Step 1: Use the property of exponents
According to the property of exponents, when multiplying two expressions with the same base, we can add the exponents. Therefore, we can rewrite the expression as:
\[ (256)^{0.16 + 0.09} \]

### Step 2: Calculate the sum of the exponents
Now, we need to add the exponents:
\[ 0.16 + 0.09 = 0.25 \]
So, we can rewrite the expression as:
\[ (256)^{0.25} \]

### Step 3: Rewrite 256 in terms of a base
Next, we can express 256 as a power of 16:
\[ 256 = 16^{2} \]
Thus, we can rewrite our expression:
\[ (16^{2})^{0.25} \]

### Step 4: Apply the power of a power property
Using the power of a power property \((a^{m})^{n} = a^{m \cdot n}\), we can simplify:
\[ (16^{2})^{0.25} = 16^{2 \times 0.25} = 16^{0.5} \]

### Step 5: Rewrite 16 in terms of a base
Next, we can express 16 as a power of 4:
\[ 16 = 4^{2} \]
So, we can rewrite our expression as:
\[ (4^{2})^{0.5} \]

### Step 6: Apply the power of a power property again
Using the power of a power property again:
\[ (4^{2})^{0.5} = 4^{2 \times 0.5} = 4^{1} = 4 \]

### Final Answer
Thus, the value of \((256)^{0.16} \times (256)^{0.09}\) is:
\[ \boxed{4} \]