`(256)^(0.16) xx (16)^(0.18)` is equal to

Options

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

Answer

To solve the expression \( (256)^{0.16} \times (16)^{0.18} \), we can follow these steps:

### Step 1: Rewrite the bases in terms of powers of 2
We know that:
- \( 256 = 2^8 \)
- \( 16 = 2^4 \)

So we can rewrite the expression as:
\[ (2^8)^{0.16} \times (2^4)^{0.18} \]

### Step 2: Apply the power of a power property
Using the property \( (a^m)^n = a^{m \cdot n} \), we can simplify each term:
\[ 2^{8 \times 0.16} \times 2^{4 \times 0.18} \]

Calculating the exponents:
- \( 8 \times 0.16 = 1.28 \)
- \( 4 \times 0.18 = 0.72 \)

So we have:
\[ 2^{1.28} \times 2^{0.72} \]

### Step 3: Combine the exponents
Using the property \( a^m \times a^n = a^{m+n} \), we can combine the exponents:
\[ 2^{1.28 + 0.72} \]

Calculating the sum of the exponents:
\[ 1.28 + 0.72 = 2.00 \]

Thus, we have:
\[ 2^{2.00} = 2^2 \]

### Step 4: Calculate the final result
Now, calculating \( 2^2 \):
\[ 2^2 = 4 \]

### Final Answer
The value of \( (256)^{0.16} \times (16)^{0.18} \) is \( 4 \).

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