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Let's simplify the given expression step-by-step using the Laws of Exponents.

The expression is:

\[
2^3 a^7 \cdot 2 a^3
\]

### Step 1: Group similar bases
First, let's group the terms with base 2 and the terms with base \(a\).

\[
(2^3 \cdot 2) \cdot (a^7 \cdot a^3)
\]

### Step 2: Apply the Laws of Exponents
- For \(2^3 \cdot 2^1\), we use the rule \(a^m \cdot a^n = a^{m+n}\). So:
  \[
  2^3 \cdot 2 = 2^{3+1} = 2^4
  \]

- For \(a^7 \cdot a^3\), we use the same exponent rule:
  \[
  a^7 \cdot a^3 = a^{7+3} = a^{10}
  \]

### Step 3: Final Expression
Now, combining the simplified terms:

\[
2^4 \cdot a^{10}
\]

Thus, the simplified expression is:

\[
\boxed{16a^{10}}
\]

Would you like more details on the steps or explanations? 

Here are some related questions:
1. How do you multiply terms with the same base and different exponents?
2. What is the value of \(2^4\)?
3. Can you explain how to combine powers of variables?
4. What would happen if the exponents were negative?
5. How do the Laws of Exponents apply to division?

**Tip:** When multiplying powers with the same base, simply add the exponents!

Simplify 2^3 a^7 · 2 a^3 using the Laws of Exponents.

Simplify the expression 2^3 a^7 · 2 a^3 step-by-step using the Laws of Exponents. Learn how to multiply terms with the same base by adding exponents. Suitable for students in Grades 7-9.

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