1. $$ \left(2 x^{-5} y^{8} z^{2}\right)\left(3 x^{2} y^{-3} z\right) $$

Question

UpStudy AI · Accepted Answer

To simplify the expression $$ \left(2 x^{-5} y^{8} z^{2}\right)\left(3 x^{2} y^{-3} z\right) $$, follow these steps:

1. **Multiply the coefficients:**
   $$
   2 \times 3 = 6
   $$

2. **Multiply the $$x$$ terms:**
   $$
   x^{-5} \times x^{2} = x^{-3}
   $$

3. **Multiply the $$y$$ terms:**
   $$
   y^{8} \times y^{-3} = y^{5}
   $$

4. **Multiply the $$z$$ terms:**
   $$
   z^{2} \times z = z^{3}
   $$

Putting it all together:
$$
6 \times x^{-3} \times y^{5} \times z^{3}
$$

To express the result with positive exponents, rewrite $$x^{-3}$$ as $$\frac{1}{x^{3}}$$:
$$
\frac{6 y^{5} z^{3}}{x^{3}}
$$

**Final Simplified Expression:**
$$
\boxed{\dfrac{6\, y^{5} z^{3}}{\,x^{3}\,}}
$$
$$ \frac{6 y^{5} z^{3}}{x^{3}} $$

1. \( \left(2 x^{-5} y^{8} z^{2}\right)\left(3 x^{2} y^{-3} z\right) \)