https://r2.erweima.ai/mathbot/image/1727036989967927c6fd5.jpg

The mathematical expression extracted from the image appears to be:

\[
\frac{3m^4 n^5 p^6}{-\frac{1}{g} m^4 n p^5}
\]

Let me simplify it step-by-step:

1. We notice the presence of the same powers of \(m^4\) in both the numerator and the denominator, so they cancel out.
2. Similarly, we can simplify the powers of \(n\) and \(p\) by subtracting the exponents.

Simplifying this:

\[
\frac{3n^5 p^6}{-\frac{1}{g} n p^5} = -3g \cdot \frac{n^5 p^6}{n p^5}
\]

Now cancel the powers of \(n\) and \(p\):

\[
= -3g \cdot n^{5-1} p^{6-5} = -3g \cdot n^4 p
\]

Thus, the simplified expression is:

\[
-3g n^4 p
\]

Would you like more details on any step or further explanation?

Here are 5 related questions to expand on this:

1. How do exponent rules apply when simplifying fractions?
2. What happens when terms cancel out in a rational expression?
3. How can negative signs affect the simplification process?
4. Could this expression represent a physical quantity in science (like volume or area)?
5. How would the expression change if the exponent of \(n\) in the denominator were different?

**Tip:** Always start by simplifying common factors and applying exponent rules carefully to avoid mistakes in large expressions.

Simplify the expression: (3m^4 n^5 p^6) / (- (1/g) m^4 n p^5).

Learn how to simplify complex exponential expressions involving fractions. This problem demonstrates key algebraic concepts such as exponent rules and fraction simplification, making it suitable for high school students in Grades 9-12.

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