3. STEM According to one estimate, the number of stars in the Milky Way Galaxy is about $$ 10^{2} \cdot 10^{3} \cdot 10^{6} $$. A. Write the number of stars in the Milky Way Galaxy as a single power. Which property of exponents did you use? B. Write the estimated number of stars in the Milky Way Galaxy without using exponents.

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Let's solve the problem step by step.

### Part A: Write the number of stars as a single power

The expression given is $$ 10^{2} \cdot 10^{3} \cdot 10^{6} $$.

To combine these powers of ten, we can use the property of exponents that states:

$$
a^{m} \cdot a^{n} = a^{m+n}
$$

Applying this property, we can add the exponents:

$$
10^{2} \cdot 10^{3} \cdot 10^{6} = 10^{(2 + 3 + 6)}
$$

Now, let's calculate the sum of the exponents:

$$
2 + 3 + 6
$$

Now, I will calculate this sum.
Calculate the value by following steps:
- step0: Calculate:
  $$2+3+6$$
- step1: Add the numbers:
  $$11$$
The sum of the exponents is $$ 11 $$. Therefore, we can write the number of stars in the Milky Way Galaxy as:

$$
10^{11}
$$

The property of exponents used here is the product of powers property: $$ a^{m} \cdot a^{n} = a^{m+n} $$.

### Part B: Write the estimated number of stars without using exponents

To express $$ 10^{11} $$ without using exponents, we can write it as:

$$
10^{11} = 10000000000
$$

Thus, the estimated number of stars in the Milky Way Galaxy is $$ 10,000,000,000 $$.
A. The number of stars is $$ 10^{11} $$. The property used is the product of powers. B. The estimated number of stars is 10,000,000,000.

STEM According to one estimate, the number of stars in the
Milky Way Galaxy is about .
A. Write the number of stars in the Milky Way Galaxy as a
single power. Which property of exponents did you use?
B. Write the estimated number of stars in the Milky Way
Galaxy without using exponents.

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STEM According to one estimate, the number of stars in the Milky Way Galaxy is about . A. Write the number of stars in the Milky Way Galaxy as a single power. Which property of exponents did you use? B. Write the estimated number of stars in the Milky Way Galaxy without using exponents.