`(256)^(0.16) xx (256)^(0.09)` is.

Options

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

Explanation

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 powers with the same base, we can add their exponents. Therefore, we can rewrite the expression as:
\[ (256)^{0.16 + 0.09} \]

**Hint:** Remember that \(a^m \times a^n = a^{m+n}\).

### Step 2: Calculate the sum of the exponents
Now, we need to calculate the sum of the exponents:
\[ 0.16 + 0.09 = 0.25 \]

**Hint:** Make sure to align the decimal points when adding decimal numbers.

### Step 3: Rewrite the expression
Now we can rewrite the expression with the new exponent:
\[ (256)^{0.25} \]

**Hint:** This step simplifies the expression significantly.

### Step 4: Convert the exponent to a fraction
The exponent \(0.25\) can be expressed as a fraction:
\[ 0.25 = \frac{25}{100} = \frac{1}{4} \]

**Hint:** Converting decimals to fractions can sometimes make calculations easier.

### Step 5: Rewrite the expression again
Now we can rewrite the expression using the fraction:
\[ (256)^{\frac{1}{4}} \]

**Hint:** The exponent \(\frac{1}{4}\) indicates the fourth root of the base.

### Step 6: Calculate the fourth root of 256
To find \((256)^{\frac{1}{4}}\), we need to determine the fourth root of 256. We can factor 256:
\[ 256 = 2^8 \]
Thus,
\[ (256)^{\frac{1}{4}} = (2^8)^{\frac{1}{4}} = 2^{8 \times \frac{1}{4}} = 2^2 = 4 \]

**Hint:** Remember that \((a^m)^n = a^{m \cdot n}\).

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