Question

repeated doubling
answer each question using any appropriate math notation.

1. if you were asked to start with the number 5 and double it three times, how would you write this problem using math notation?
2. if you were asked to start with the number 5 and double it nine times, how would you write this problem using math notation?
3. if you were asked to start with the number 5 and double it one hundred times, how would you write this problem using math notation?

Explanation:

Step1: Define repeated doubling rule

Doubling a number $n$ times means multiplying by $2^n$.

Step2: Apply to 3 doublings

Start with 5, multiply by $2^3$.
<Expression> $5 \times 2^3$ </Expression>

Step3: Apply to 9 doublings

Start with 5, multiply by $2^9$.
<Expression> $5 \times 2^9$ </Expression>

Step4: Apply to 100 doublings

Start with 5, multiply by $2^{100}$.
<Expression> $5 \times 2^{100}$ </Expression>

Answer:

1. $5 \times 2^3$
2. $5 \times 2^9$
3. $5 \times 2^{100}$