Chapter 6.2, Problem 9E

To determine

To simplify the expression

Answer to Problem 9E

The solution of the expression is $3e^{3x}$

Explanation of Solution

Given information:

Consider the given information,

  $\sqrt{9e^{6x}}$

CALCULATION:

Calculate the expression as,

  $\begin{array}{l}=\sqrt{\left(3\times 3\right)e^{\left(2\times 3\right)x}}\\ =\sqrt{{\left(3\right)}^2{\left(e^{3x}\right)}^2}\end{array}$

As from the power property, the expression get changed as any number to the power of e can be changed to the power of the whole.

Removing, the square root we get - $3e^{3x}$

As, the power and the square root gets cancelled.

Therefore, the expression obtained is $3e^{3x}$ .