https://file.aiquickdraw.com/mathbot/file/172731478839468u8mdeu.jpg

The expression given in the image is:

\[
(3.0 \times 10^8)^3
\]

To solve this, we'll use the property of exponents: \((a \times b)^n = a^n \times b^n\).

### Step-by-Step Solution:

1. Expand the expression using the exponent rule:

   \[
   (3.0 \times 10^8)^3 = (3.0)^3 \times (10^8)^3
   \]

2. Calculate \((3.0)^3\):

   \[
   (3.0)^3 = 3.0 \times 3.0 \times 3.0 = 27.0
   \]

3. Calculate \((10^8)^3\) using the power rule \( (10^a)^b = 10^{a \times b} \):

   \[
   (10^8)^3 = 10^{8 \times 3} = 10^{24}
   \]

4. Combine the results:

   \[
   27.0 \times 10^{24}
   \]

Therefore, the simplified form of the expression is:

\[
\boxed{2.7 \times 10^{25}}
\]

Would you like further details or have any questions?

### Related Questions:
1. How do you simplify expressions involving exponents with different bases?
2. What are the properties of exponents when multiplying or dividing powers?
3. How do you simplify expressions like \((a \times 10^n)^m\) in scientific notation?
4. What are some practical applications of exponential calculations?
5. How can you use a calculator to solve expressions involving powers of ten?

**Tip:** Remember that when working with scientific notation, always keep track of the exponents and apply the rules of exponents carefully!

Learn how to simplify the expression (3.0 × 10^8)^3 with a detailed, step-by-step explanation. This problem covers key exponentiation concepts and scientific notation, suitable for students in Grades 9-12.

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