Question

$2^{1000}-2^{999}=$

• A. $2^9$
• B. $2^{11}$
• C. $2^{111}$
• D. $2^{999}$

Answer 1

Answer:

$2^{999}$

The value of $2^{1000} - 2^{999}$ is $2^{999}$.

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• Find the common factor: Look for the lowest power of 2 present in both terms, which is $2^{999}$.

• Factor it out: Rewrite the expression by pulling out $2^{999}$:
  $2^{1000} - 2^{999} = 2^{999} \cdot (2^1 - 1)$

• Simplify inside the brackets: Since $2^1 = 2$, the expression becomes:
  $2^{999} \cdot (2 - 1)$

• Final calculation:
  $2^{999} \cdot 1 = \mathbf{2^{999}}$