https://file.aiquickdraw.com/mathbot/file/17290421717654kctzf3j.jpg

The given expression is:

\[
\frac{u^{-5}}{\frac{-7}{u^5} \cdot \frac{-13}{u^5}}
\]

Let's simplify it step by step.

### Step 1: Simplifying the denominator
The denominator is the product of two fractions:

\[
\frac{-7}{u^5} \cdot \frac{-13}{u^5} = \frac{-7 \cdot -13}{u^5 \cdot u^5} = \frac{91}{u^{10}}
\]

So, the expression becomes:

\[
\frac{u^{-5}}{\frac{91}{u^{10}}}
\]

### Step 2: Dividing by a fraction
To divide by a fraction, multiply by its reciprocal:

\[
\frac{u^{-5}}{\frac{91}{u^{10}}} = u^{-5} \cdot \frac{u^{10}}{91} = \frac{u^{-5} \cdot u^{10}}{91}
\]

### Step 3: Simplifying the powers of \( u \)
Using the laws of exponents \( u^{-5} \cdot u^{10} = u^{10 - 5} = u^5 \), the expression simplifies to:

\[
\frac{u^5}{91}
\]

Thus, the simplified expression is:

\[
\frac{u^5}{91}
\]

Would you like any further clarification or details on this simplification?

Here are 5 related questions to further your understanding:
1. How do you multiply two fractions with variables?
2. What are the rules for multiplying powers of the same base?
3. How would the result change if the exponents were different?
4. Can you apply the same process for division with higher powers of variables?
5. How can this expression be used in solving equations?

**Tip**: Always check the signs and powers carefully when multiplying fractions to avoid mistakes!

Simplify the expression: (u^(-5)) / ((-7 / u^5) * (-13 / u^5))

Learn how to simplify the fractional expression (u^(-5)) / ((-7/u^5) * (-13/u^5)) using the laws of exponents and multiplication of fractions. This problem focuses on exponent rules and basic algebraic simplifications, suitable for students in Grades 8-10.

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