https://file.aiquickdraw.com/mathbot/file/1726101627766rlh3s457.jpg

Let's analyze the problem:

You are asked to find which expression is equivalent to \(\frac{10^{33}}{10}\).

### Step 1: Simplify the Expression
The given expression is \(\frac{10^{33}}{10}\). We can use the property of exponents that states:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
So, applying this rule:
\[
\frac{10^{33}}{10} = 10^{33-1} = 10^{32}
\]

### Step 2: Compare the Simplified Expression with the Given Choices
Now, we check which of the provided options is equivalent to \(10^{32}\):

1. \(2^{32} \cdot 5^{32}\) - This expression is equivalent to \( (2 \cdot 5)^{32} = 10^{32} \), which matches our simplification.
2. \(10^{33}\) - This is not equivalent to \(10^{32}\).
3. \(\frac{1}{10^{33}}\) - This is not equivalent to \(10^{32}\).
4. \(10^{34}\) - This is not equivalent to \(10^{32}\).

### Conclusion:
The correct choice is **\(2^{32} \cdot 5^{32}\)**.

Would you like more details, or do you have any questions?

Here are some related questions:
1. How can you use the properties of exponents to simplify other expressions?
2. What is the general form of the multiplication property of exponents?
3. How do you handle exponent rules when the bases are different?
4. What happens when you divide powers with the same base but different exponents?
5. How can you apply exponent rules to solve equations?

**Tip:** Remember that \(2^{32} \times 5^{32}\) simplifies to \( (2 \times 5)^{32} = 10^{32}\). This can be a useful trick in problems involving powers of 10.

Which expression is equivalent to (10^33) / 10?

Learn how to simplify the expression (10^33) / 10 using the properties of exponents. This problem demonstrates the exponent division rule and explores different ways to express the solution. Suitable for Grades 8-10.

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