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The equation provided is:

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

To solve for the missing exponent \(x\):

We know that negative exponents correspond to the reciprocal of the base raised to the positive of that exponent. In other words:

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

By comparing both sides, we can see that the missing exponent \(x\) must be \(5\). Therefore, the missing power is \(x = 5\).

Do you want more details, or do you have any further questions?

Here are 5 questions to expand on this concept:

1. What are the properties of exponents that apply when multiplying or dividing powers of the same base?
2. How do you simplify expressions with negative exponents?
3. What happens when you raise a number to the power of zero?
4. Can you solve a similar equation but with different numbers and exponents?
5. What is the relationship between fractional exponents and roots?

**Tip:** Always remember that a negative exponent turns the expression into a reciprocal!

What is the missing power in the equality 12^-5 = 1 / 12^x?

Solve for the missing power in the equation 12^-5 = 1 / 12^x. Learn about negative exponents and reciprocal relationships in this algebraic concept. Suitable for students in Grades 6-8.

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