Simplify the following expression. Write the result using positive exponents only. $$ \left(-7 x^{2} y^{-4}\right)\left(7 x^{-3} y^{7}\right) $$

Question

UpStudy AI · Accepted Answer

To simplify the expression $$ \left(-7 x^{2} y^{-4}\right)\left(7 x^{-3} y^{7}\right) $$ with only positive exponents, follow these steps:

1. **Multiply the constants:**
   $$
   (-7) \times 7 = -49
   $$

2. **Multiply the $$ x $$-terms by adding the exponents:**
   $$
   x^{2} \times x^{-3} = x^{2-3} = x^{-1}
   $$

3. **Multiply the $$ y $$-terms by adding the exponents:**
   $$
   y^{-4} \times y^{7} = y^{-4+7} = y^{3}
   $$

Putting it all together:
$$
-49 \times x^{-1} \times y^{3} = -49 y^{3} x^{-1}
$$

4. **Rewrite the expression with positive exponents by moving $$ x^{-1} $$ to the denominator:**
   $$
   \frac{-49 y^{3}}{x}
   $$

**Final Answer:**
$$
\boxed{\dfrac{-49\,y^{3}}{\,x\,}}
$$
$$ \frac{-49 y^{3}}{x} $$

Simplify the following expression. Write the result using positive exponents only. \( \left(-7 x^{2} y^{-4}\right)\left(7 x^{-3} y^{7}\right) \)