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The problem asks which expression is equivalent to \( 12^{-7} \times 12^2 \).

To solve this, we use the properties of exponents, specifically:

\[
a^m \times a^n = a^{m+n}
\]

Here, \( m = -7 \) and \( n = 2 \), so:

\[
12^{-7} \times 12^2 = 12^{-7 + 2} = 12^{-5}
\]

Thus, the equivalent expression is \( 12^{-5} \). This matches the option "1/12^5", since \( 12^{-5} \) can also be written as:

\[
12^{-5} = \frac{1}{12^5}
\]

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

### Related Questions:
1. What is the rule for multiplying powers with the same base?
2. How would you simplify \( a^{-3} \times a^4 \)?
3. What is the significance of negative exponents in expressions?
4. How do you handle division with exponents, such as \( \frac{a^5}{a^3} \)?
5. What happens when you raise a power to another power, like \( (a^3)^2 \)?

**Tip:** When multiplying terms with the same base, remember to add the exponents!

Which expression is equivalent to 12^(-7) * 12^2?

Learn how to simplify the exponential expression 12^(-7) * 12^2 using exponent rules. This solution explains step-by-step how to apply the rule a^m * a^n = a^(m+n), leading to the result 12^(-5). Suitable for students in Grades 7-9.

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