6. $$ \frac{p^{4} q^{4}}{r^{4} t^{4}} $$

Question

UpStudy AI · Accepted Answer

1. Start with the expression:
   
   $$
   \frac{p^{4}q^{4}}{r^{4}t^{4}}
   $$

2. Recognize that the power rule for a product allows us to write:
   
   $$
   p^{4}q^{4} = (pq)^{4} \quad \text{and} \quad r^{4}t^{4} = (rt)^{4}
   $$

3. Substitute these into the original expression:
   
   $$
   \frac{(pq)^{4}}{(rt)^{4}}
   $$

4. Apply the quotient of powers rule, which states that:
   
   $$
   \frac{a^{n}}{b^{n}} = \left(\frac{a}{b}\right)^{n}
   $$
   
   Therefore:
   
   $$
   \frac{(pq)^{4}}{(rt)^{4}} = \left(\frac{pq}{rt}\right)^{4}
   $$

Thus, the simplified form is:

$$
\boxed{\left(\frac{pq}{rt}\right)^{4}}
$$
$$ \left(\frac{pq}{rt}\right)^{4} $$

6. \( \frac{p^{4} q^{4}}{r^{4} t^{4}} \)

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