`(256)^(0.16)xx(4)^(0.36)` is equal to

Options

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

Answer

To solve the expression \((256)^{0.16} \times (4)^{0.36}\), we can follow these steps:

### Step 1: Rewrite 256 in terms of base 4
We know that:
\[ 256 = 4^4 \]
Thus, we can rewrite the expression as:
\[ (4^4)^{0.16} \times (4)^{0.36} \]

### Step 2: Apply the power of a power property
Using the property \((a^m)^n = a^{m \cdot n}\), we can simplify \((4^4)^{0.16}\):
\[ (4^4)^{0.16} = 4^{4 \times 0.16} = 4^{0.64} \]

### Step 3: Combine the powers of 4
Now we can combine the two terms:
\[ 4^{0.64} \times 4^{0.36} \]
Using the property \(a^m \times a^n = a^{m+n}\), we can add the exponents:
\[ 4^{0.64 + 0.36} = 4^{1.00} \]

### Step 4: Simplify the expression
Since \(4^{1.00} = 4\), we find that:
\[ (256)^{0.16} \times (4)^{0.36} = 4 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{4} \]

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