Explain why $\sqrt[k]{\mathrm{x}^{\mathrm{k}}}=|\mathrm{x}|$ when $\mathrm{k}$ is even but $\sqrt[k]{\mathrm{x}^{\mathrm{k}}}=\mathrm{x}$ when $\mathrm{k}$ is odd.

Question

Quizplus · Accepted Answer

The Answer of Explain why $\sqrt[k]{\mathrm{x}^{\mathrm{k}}}=|\mathrm{x}|$ when $\mathrm{k}$ is even but $\sqrt[k]{\mathrm{x}^{\mathrm{k}}}=\mathrm{x}$ when $\mathrm{k}$ is odd.

Explain Why xkk=∣x∣\sqrt[k]{\mathrm{x}^{\mathrm{k}}}=|\mathrm{x}|kxk​=∣x∣ When k\mathrm{k}k Is Even But xkk=x\sqrt[k]{\mathrm{x}^{\mathrm{k}}}=\mathrm{x}kxk​=x When k\mathrm{k}k Is Odd

Explain Why $\sqrt[k]{\mathrm{x}^{\mathrm{k}}}=|\mathrm{x}|$ When $\mathrm{k}$ Is Even But $\sqrt[k]{\mathrm{x}^{\mathrm{k}}}=\mathrm{x}$ When $\mathrm{k}$ Is Odd