Chapter SH, Problem 7.14EP

To determine

To simplify

  $\sqrt[5]{0.00001}$ .

Answer to Problem 7.14EP

  

Explanation of Solution

Given information:

Expression

  $\sqrt[5]{0.00001}$

Calculation:

= $\sqrt[5]{0.00001}$

Rewrite

  $\sqrt[5]{\frac{1}{{10}^5}}$

Using identity

  $\sqrt[5]{a}=a^{\frac{1}{5}}$

Then,

  $={\left(\frac{1}{{10}^5}\right)}^{\frac{1}{5}}$

So,

  $={\left({10}^{-5}\right)}^{\frac{1}{5}}$

On solving,

  $={10}^{-5\times \frac{1}{5}}$

On solving,

  $={10}^{-1}$

On solving,

  $=\frac{1}{{10}^{}}$

Hence, simplified form is $\frac{1}{{10}^{}}$ .