Chapter 7.5, Problem 41P

Reasoning Show that $\sqrt[4]{a^2}=\sqrt{a}$ by rewriting $\sqrt[4]{a^2}$ in exponential form.

To determine

To find: The equation given is true by writing the left side in exponential form.

Answer to Problem 41P

The equation given is true.

Explanation of Solution

Given information: The equation given, $\sqrt[4]{a^2}=\sqrt{a}$ .

Calculation:

The equation given, $\sqrt[4]{a^2}=\sqrt{a}$ .

By writing the left side in exponential form,

$\begin{array}{}$ \sqrt[4]{a^2}$$ ={\left(a^2\right)}^{\frac{1}{4}}$$ ={(a)}^{2\cdot \frac{1}{4}}$$ ={(a)}^{\frac{2}{4}}$$ ={(a)}^{\frac{1}{2}}=\sqrt{a}$\end{array}$

  $\therefore$ The equation given is true.