Question: Find the following fraction in simplest form, only using positive exponents
$\frac{(2j^3p)^{-1}}{10j^6}$
1. **State the problem:** Simplify the fraction $$\frac{(2j^3p)^{-1}}{10j^6}$$ so that all exponents are positive.
2. **Recall the rule for negative exponents:** $$a^{-n} = \frac{1}{a^n}$$.
3. Apply the negative exponent rule to the numerator:
$$ (2j^3p)^{-1} = \frac{1}{2j^3p} $$
4. Rewrite the original expression:
$$ \frac{\frac{1}{2j^3p}}{10j^6} = \frac{1}{2j^3p} \times \frac{1}{10j^6} $$
5. Multiply the denominators:
$$ = \frac{1}{2j^3p \times 10j^6} = \frac{1}{20j^{3+6}p} = \frac{1}{20j^9p} $$
6. The expression is now:
$$ \frac{1}{20j^9p} $$
7. Since all exponents are positive and the expression is simplified, this is the final answer.
**Final answer:** $$\frac{1}{20j^9p}$$