https://file.aiquickdraw.com/mathbot/file/1727310038651ilmlzqla.jpg

The expression given in the image is:

\[
\frac{(15^x \cdot 7^3)}{15^2}
\]

We are asked to find an equivalent expression from the choices provided.

### Step 1: Simplify the expression.

To simplify, we will apply the properties of exponents:

\[
\frac{15^x \cdot 7^3}{15^2}
\]

This is a division of exponents with the same base, so we subtract the exponents of \(15\):

\[
15^{x-2} \cdot 7^3
\]

### Step 2: Compare with the choices.

Now we look for an answer that matches this simplified form.

1. **Option (a)**: \(15^2 \cdot 7^9\)
2. **Option (b)**: \(15^2 \cdot 7^{18}\)
3. **Option (c)**: \(15^5 \cdot 7^9\)
4. **Option (d)**: \(15^{10} \cdot 7^{18}\)

### Conclusion:

Since the exponent of \(15\) in the simplified form is \(x - 2\) and the exponent of \(7\) is 3, none of the answer choices directly match the simplified form as written. It seems there might be a clarification needed about the value of \(x\). Could you confirm if \(x = 5\)? This would make the expression match one of the options, likely (c).

Which expression is equivalent to (15^x * 7^3) / 15^2?

Explore how to simplify the expression (15^x * 7^3) / 15^2 using exponent rules. This problem involves key algebraic concepts such as the exponent division rule and is suitable for students in Grades 8-10.

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