Simplify the expression completely: $$ \frac{\left(2 x^{3}\right)^{2}}{x^{-5}}=\square $$

Question

UpStudy AI · Accepted Answer

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

1. **Expand the Numerator:**

$$
   \left(2x^{3}\right)^{2} = 2^{2} \cdot \left(x^{3}\right)^{2} = 4x^{6}
   $$

2. **Rewrite the Expression:**

$$
   \frac{4x^{6}}{x^{-5}}
   $$

3. **Simplify the Division by a Negative Exponent:**

Recall that dividing by $$ x^{-5} $$ is the same as multiplying by $$ x^{5} $$:

$$
   4x^{6} \cdot x^{5} = 4x^{6+5} = 4x^{11}
   $$

Alternatively, using the properties of exponents:

$$
   \frac{x^{6}}{x^{-5}} = x^{6 - (-5)} = x^{11}
   $$

4. **Final Simplified Expression:**

$$
   4x^{11}
   $$

**Answer:** $$4x^{11}$$
$$4x^{11}$$

Simplify the expression completely: \( \frac{\left(2 x^{3}\right)^{2}}{x^{-5}}=\square \)