Question

$(256)^{0.16} \times (256)^{0.09} = ?$}

• A. 16
• B. 4
• C. 256.25
• D. 64

Hint:

Convert decimals to fractions to simplify powers easily.

Answer 1

The Correct Option is B

Concept: Use law of exponents: \[ a^m \cdot a^n = a^{m+n} \]
Step 1: Add exponents.
\[ (256)^{0.16 + 0.09} = (256)^{0.25} \]
Step 2: Convert to fraction.
\[ 0.25 = \frac{1}{4} \Rightarrow (256)^{1/4} \]
Step 3: Evaluate.
\[ 256 = 2^8 \Rightarrow (2^8)^{1/4} = 2^2 = 4 \]
Hence, the value is 4.