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

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:** \[ \boxed{\dfrac{-49\,y^{3}}{\,x\,}} \]