Question

Simplify: $\sqrt[4]{16}-6\sqrt[3]{343}+18\times \sqrt[5]{243}-\sqrt{196}$

Answer 1

Let us simplify the expression by simplifying each term separately.
$$\begin{gathered} \sqrt[4]{16}=\sqrt[4]{2\times 2\times 2\times 2}=2 \\ \sqrt[3]{343}=\sqrt[3]{7\times 7\times 7}=7 \\ \sqrt[5]{243}=\sqrt[5]{3\times 3\times 3\times 3\times 3}=3 \\ \sqrt{196}=\sqrt{14\times 4}=14 \end{gathered}$$
Therefore
$$\begin{gathered} \sqrt[4]{16}-6\sqrt[3]{343}+18\times \sqrt[5]{243}-\sqrt{196} \\ =2-6\times 7+18\times 3-14 \\ =2-42+54-14 \\ =56-56 \\ =0 \end{gathered}$$
Hence, $\sqrt[4]{16}-6\sqrt[3]{343}+18\times \sqrt[5]{243}-\sqrt{196}=0$.