Chapter SH, Problem 7.12EP

To determine

To write in exponential form

  $3\sqrt{2xy{z}^2}$ .

Answer to Problem 7.12EP

  $3z\left({(2xy)}^{\frac{1}{2}}\right)$

Explanation of Solution

Given information:

Expression

  $3\sqrt{2xy{z}^2}$

Calculation:

  $3\sqrt{2xy{z}^2}$

Using identity

  $k\sqrt{a}=k{\left(a\right)}^{\frac{1}{2}}$

Where, k is constant

From question

  $k=3$

  $a=\sqrt{2xy{z}^2}$

  $3\sqrt{2xy{z}^2}=3{\left(2xy{z}^2\right)}^{\frac{1}{2}}$

On inserting half in the bracket

  $=3\left({(2)}^{\frac{1}{2}}{(xy)}^{\frac{1}{2}}{(z^2)}^{\frac{1}{2}}\right)$

On solving,

  $=3z\left({(2xy)}^{\frac{1}{2}}\right)$

Hence, exponential form is $3z\left({(2xy)}^{\frac{1}{2}}\right)$ .