Simplify the following expression. Write the result using positive exponents only.

Ask by Hardy Bob. in the United States

Jan 23,2025

Question

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

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.