https://file.aiquickdraw.com/mathbot/file/1726567072106sequk5zw.jpg

The expression in the image shows \( x^{-5} \times x^2 \).

To simplify this, we apply the rule of exponents, which states that when multiplying powers with the same base, we add the exponents:

\[
x^{-5} \times x^2 = x^{-5 + 2} = x^{-3}
\]

So, the simplified expression is:

\[
x^{-3}
\]

Would you like further details or have any questions on this?

Here are 5 related questions to consider:
1. How do you simplify an expression like \( (x^{-3})^2 \)?
2. What is the rule for dividing exponents with the same base?
3. How do you convert a negative exponent into a fraction?
4. What happens when you multiply a term with zero as the exponent, such as \( x^0 \)?
5. How would you apply the same exponent rules to numbers with different bases?

**Tip:** A negative exponent, such as \( x^{-n} \), can be rewritten as \( \frac{1}{x^n} \).

Learn how to simplify the exponent expression x^-5 * x^2 using the law of exponents. This step-by-step solution adds the exponents to give x^-3, suitable for students in Grades 7-9.

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