❓❓ Subtraction of powers ❓❓ - Free Printable

We are tasked with solving the expression \( 2^{19} - 2^{18} \) and identifying the correct answer from the given options:

- \( \text{a) } 2 \)
- \( \text{b) } 2\sqrt{2} \)
- \( \text{c) } 2^{18} \)
- \( \text{d) } 2^{37} \)

Step-by-Step Solution:

1. Factor out the common term:
Both terms in the expression \( 2^{19} \) and \( 2^{18} \) have a common factor of \( 2^{18} \). We can factor this out:
\[
2^{19} - 2^{18} = 2^{18} \cdot 2^1 - 2^{18} \cdot 1
\]
This simplifies to:
\[
2^{19} - 2^{18} = 2^{18} (2 - 1)
\]

2. Simplify the expression inside the parentheses:
\[
2 - 1 = 1
\]
So the expression becomes:
\[
2^{18} \cdot 1 = 2^{18}
\]

3. Identify the correct answer:
The simplified result is \( 2^{18} \), which matches option \( \text{c) } 2^{18} \).

Final Answer:

\[
\boxed{c}
\]