`(256)^(0. 16)xx(256)^(0. 09)=?`

Options

A. 4
B. 16
C. 64
D. -4

Explanation

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

### Step 1: Apply the Law of Exponents
When multiplying two powers with the same base, we can add their exponents. Thus, we can rewrite the expression as:
\[ (256)^{0.16 + 0.09} \]

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

### Step 3: Rewrite 0.25 as a Fraction
We can express \(0.25\) as a fraction:
\[ 0.25 = \frac{25}{100} = \frac{1}{4} \]
Thus, we can rewrite the expression as:
\[ (256)^{\frac{1}{4}} \]

### Step 4: Factor 256
Next, we need to express \(256\) as a power of \(2\). We can find that:
\[ 256 = 2^8 \]
So, we can substitute this into our expression:
\[ (2^8)^{\frac{1}{4}} \]

### Step 5: Apply the Power of a Power Rule
Using the power of a power rule \((a^m)^n = a^{m \cdot n}\), we can simplify:
\[ (2^8)^{\frac{1}{4}} = 2^{8 \cdot \frac{1}{4}} = 2^{2} \]

### Step 6: Calculate the Final Value
Finally, we can calculate \(2^2\):
\[ 2^2 = 4 \]

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