Simplify the expression completely: $$ \frac{x^{-3}}{y^{-4}}=\square $$

Question

UpStudy AI · Accepted Answer

To simplify the expression $$ \frac{x^{-3}}{y^{-4}} $$, follow these steps:

1. **Apply the Negative Exponent Rule:**
   - $$ x^{-3} = \frac{1}{x^3} $$
   - $$ y^{-4} = \frac{1}{y^4} $$

2. **Rewrite the Original Expression:**
   $$
   \frac{x^{-3}}{y^{-4}} = \frac{\frac{1}{x^3}}{\frac{1}{y^4}} 
   $$

3. **Simplify the Division of Fractions:**
   $$
   \frac{\frac{1}{x^3}}{\frac{1}{y^4}} = \frac{1}{x^3} \times \frac{y^4}{1} = \frac{y^4}{x^3}
   $$

So, the simplified form of the expression is:

$$
\frac{y^4}{x^3}
$$

**Answer:** $$\dfrac{y^{4}}{\,x^{3}\,}$$
The simplified form of the expression is $$ \frac{y^{4}}{x^{3}} $$.

Simplify the expression completely: \( \frac{x^{-3}}{y^{-4}}=\square \)