Chapter 4.3, Problem 9E

Solution

To calculate: $\sqrt{9e^6}$

The solution of the given problem is $3e^3$ .

Given information: Compute the given expression $\sqrt{9e^6}$ .

Calculation:

solve this problem in steps.

Step 1: Write the problem in two parts

  $\sqrt{9}$ and $\sqrt{e^6}$

Step 2: Check what are the coefficients, exponents and base.

An exponent is a number or letter written above and to the right of a mathematical expression called the base.

Coefficient is a number multiplied by a variable.

A base is a number which gets multiplied when using an exponent.

Here, base is $e^{}$ .

Here, exponents is same for both the parts that is $\frac{1}{2}$ .

The coefficient is $\sqrt{9}$ .

Step 3: Check which property of exponents goes with the given question.

The property of power of a product rule states that simplify a power of a power by multiplying the exponents and keeping the same base.

  $\sqrt{9}=3$

And,

  $\sqrt{e^6}=e^3$ ...... (1)

Reason for equation (1) is $e^3·e^3=e^6$

The final answer is $3e^3$