Assume the variable represents a nonzer $$ \frac{r^{-4}}{r^{7}}=\square \square \square $$

Question

UpStudy AI · Accepted Answer

To simplify the expression $$\frac{r^{-4}}{r^{7}}$$, follow these steps:

1. **Use the Law of Exponents for Division:**
   
   When dividing like bases, subtract the exponents:
   $$
   \frac{r^{-4}}{r^{7}} = r^{-4 - 7} = r^{-11}
   $$

2. **Express with a Positive Exponent (Optional):**
   
   If preferred, you can rewrite the expression with a positive exponent:
   $$
   r^{-11} = \frac{1}{r^{11}}
   $$

**Final Answer:**
$$
\frac{r^{-4}}{r^{7}} = r^{-11}
$$
or equivalently,
$$
\frac{1}{r^{11}}
$$
$$ \frac{r^{-4}}{r^{7}} = r^{-11} \quad \text{or} \quad \frac{1}{r^{11}} $$

Assume the variable represents a nonzer \[ \frac{r^{-4}}{r^{7}}=\square \square \square \]

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