Mathematics: What is the simplified form of the following expression?

What is the simplified form of the following expression?

Ответ:

Gabby7047

13.01.2022

$\large\boxed{7\sqrt[3]{2x}-3\sqrt[3]{16x}-3\sqrt[3]{8x}=\sqrt[3]{2x}-6\sqrt[3]{x}}$

Step-by-step explanation:

$7\sqrt[3]{2x}-3\sqrt[3]{16x}-3\sqrt[3]{8x}\\\\=7\sqrt[3]{2x}-3\sqrt[3]{(8)(2x)}-3\sqrt[3]{8x}\qquad\text{use}\ \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\\\\=7\sqrt[3]{2x}-3\sqrt[3]8\cdot\sqrt[3]{2x}-3\sqrt[3]8\cdot\sqrt[3]{x}\\\\=7\sqrt[3]{2x}-3(2)\sqrt[3]{2x}-3(2)\sqrt[3]{x}\\\\=7\sqrt[3]{2x}-6\sqrt[3]{2x}-6\sqrt[3]{x}\\\\=\sqrt[3]{2x}-6\sqrt[3]{x}$