Simplify : `2^(4) div 2^(-1)`
A. 1/32
B. 16
C. 32
D. 8

Options

A. B
B. A
C. C
D. D

Answer

To simplify the expression \( 2^{4} \div 2^{-1} \), we can follow these steps:

### Step 1: Rewrite the Division as Subtraction of Exponents
Using the property of exponents that states \( a^m \div a^n = a^{m-n} \), we can rewrite the expression:
\[ 2^{4} \div 2^{-1} = 2^{4 - (-1)} \]

### Step 2: Simplify the Exponent
Now, simplify the exponent:
\[ 4 - (-1) = 4 + 1 = 5 \]
Thus, we have:
\[ 2^{4} \div 2^{-1} = 2^{5} \]

### Step 3: Calculate \( 2^{5} \)
Now, calculate \( 2^{5} \):
\[ 2^{5} = 2 \times 2 \times 2 \times 2 \times 2 \]
Calculating this step-by-step:
- \( 2 \times 2 = 4 \)
- \( 4 \times 2 = 8 \)
- \( 8 \times 2 = 16 \)
- \( 16 \times 2 = 32 \)

### Final Answer
Thus, \( 2^{5} = 32 \).

The correct answer is **C. 32**.

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