https://file.aiquickdraw.com/mathbot/file/1727188237872e5i8j0pm.jpg

The expression in the image is:

\[
a \cdot 2^7 \times 2^2 \div 2^{-8}
\]

Let’s simplify this step by step:

### Step 1: Combine the powers of 2
Use the properties of exponents:

\[
a \cdot 2^7 \times 2^2 \div 2^{-8}
\]

Multiplication of exponents with the same base means adding the exponents:
\[
2^7 \times 2^2 = 2^{7 + 2} = 2^9
\]

For division, subtract the exponents:
\[
2^9 \div 2^{-8} = 2^{9 - (-8)} = 2^{9 + 8} = 2^{17}
\]

### Step 2: Simplified expression
The expression now becomes:
\[
a \cdot 2^{17}
\]

This is the simplified form of the given expression.

Would you like more details or have any further questions?

Here are some related questions:
1. What are the properties of exponents used in this problem?
2. How do you simplify expressions involving negative exponents?
3. Can you explain how multiplication and division interact with exponents?
4. What would happen if the exponents had different bases?
5. How would the result change if the base was different (e.g., base 3)?

**Tip:** Always combine like terms when working with exponents to make simplification easier!

Simplify the expression: a · 2^7 × 2^2 ÷ 2^(-8)

Simplify the expression a · 2^7 × 2^2 ÷ 2^(-8) using the properties of exponents. Learn step-by-step how to combine powers through multiplication and division. This problem is ideal for students in Grades 8-10, covering essential exponent rules.

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