The simplified expression, written properly with square roots, is:
![\[ -7ab \sqrt[3]{a \cdot b^2} \]](https://img.qammunity.org/2023/formulas/mathematics/college/gfwaf81fh6dwf9ycdukhin124xh3c769vw.png)
The original expression is:
![\[ 2ab \sqrt[3]{192a \cdot b^2} - 5 \sqrt[3]{81a^4 \cdot b^5} \]](https://img.qammunity.org/2023/formulas/mathematics/college/xhe3g9sm171unxgxtrdc2gwj6hkuxwc8gi.png)
Now, rewrite the expressions inside the cube roots using prime factorization:
![\[ 2ab \sqrt[3]{3 \cdot 4^3 \cdot a \cdot b^2} - 5 \sqrt[3]{3 \cdot 3^3 \cdot a^4 \cdot b^5} \]](https://img.qammunity.org/2023/formulas/mathematics/college/ousk4bgr3yw8jn9yf5g27k58a4flpeugch.png)
Evaluate the cube roots:
![\[ 2ab \cdot 4 \sqrt[3]{a \cdot b^2} - 5 \cdot 3ab \sqrt[3]{a \cdot b^2} \]](https://img.qammunity.org/2023/formulas/mathematics/college/v04ejutqss1myp2sljueolwr4j03gxm65e.png)
Evaluate the products:
![\[ 8ab \sqrt[3]{a \cdot b^2} - 15ab \sqrt[3]{a \cdot b^2} \]](https://img.qammunity.org/2023/formulas/mathematics/college/f1ikb6nyox23vihstij3jiilwdjz1el9sf.png)
Combine the terms:
![\[ -7ab \sqrt[3]{a \cdot b^2} \]](https://img.qammunity.org/2023/formulas/mathematics/college/gfwaf81fh6dwf9ycdukhin124xh3c769vw.png)
Therefore, the simplified expression, written properly with square roots, is:
![\[ -7ab \sqrt[3]{a \cdot b^2} \]](https://img.qammunity.org/2023/formulas/mathematics/college/gfwaf81fh6dwf9ycdukhin124xh3c769vw.png)