Simplify. Use positive exponents for any variables. Assume that all bases are not equal to 0

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Simplify. Use positive exponents for any variables. Assume that all bases are not equal to 0 $$ \frac{p^{-2}}{q^{-9}} $$

UpStudy AI · Accepted Answer

To simplify the expression $$ \frac{p^{-2}}{q^{-9}} $$ and ensure all exponents are positive, follow these steps:

1. **Convert Negative Exponents to Positive:**
   - Recall that $$ a^{-n} = \frac{1}{a^n} $$.
   - Apply this to both $$ p^{-2} $$ and $$ q^{-9} $$:
     $$
     \frac{p^{-2}}{q^{-9}} = \frac{\frac{1}{p^2}}{\frac{1}{q^9}}
     $$

2. **Simplify the Fraction:**
   - When you divide by a fraction, it's the same as multiplying by its reciprocal:
     $$
     \frac{\frac{1}{p^2}}{\frac{1}{q^9}} = \frac{1}{p^2} \times \frac{q^9}{1} = \frac{q^9}{p^2}
     $$

3. **Final Simplified Form:**
   - The expression with all positive exponents is:
     $$
     \frac{q^9}{p^2}
     $$

**Answer:** 
$$\dfrac{q^{9}}{\,p^{\,2}\,}$$
$$\frac{q^{9}}{p^{2}}$$

Simplify. Use positive exponents for any variables. Assume that all bases are not equal to 0

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