Simplify  $\left(-4\sqrt[3]{29}\right)\cdot\left(-3\sqrt[3]{38}\right)$(−43√29)·(−33√38)​ .The simplified expression is

1. Break Down the Problem

We need to simplify the expression $\left(-4\sqrt[3]{29}\right)\cdot\left(-3\sqrt[3]{38}\right)$.

2. Relevant Concepts

To simplify this expression, we will use the properties of multiplication and radicals. Specifically, we will focus on:

• The product of two negative numbers is a positive number.
• The product of the coefficients and the product of the radicals.

3. Analysis and Detail

Let's break it down into parts.

1. Coefficients: $-4 \cdot -3 = 12$

2. Radicals: $\sqrt[3]{29} \cdot \sqrt[3]{38} = \sqrt[3]{29 \cdot 38}$

Now, we compute $29 \cdot 38$: $29 \cdot 38 = 1102$

Putting it all together, we have: $\left(-4\sqrt[3]{29}\right)\cdot\left(-3\sqrt[3]{38}\right) = 12 \cdot \sqrt[3]{1102}$

4. Verify and Summarize

We have arrived at the simplified expression. The calculations are consistent with the properties of multiplication and radicals.

Final Answer

The simplified expression is: $12\sqrt[3]{1102}$