Chapter 4.3, Problem 14E

Solution

To calculate: The value of $\frac{6e^{4x}}{8e}$.

The value of $\frac{6e^{4x}}{8e}$ is $\frac{3}{4}\left(e^{4x+1}\right)$.

Given information: Compute the given expression $\frac{6e^{4x}}{8e}$.

Calculation:

Step 1: Write the problem in simplified form $\frac{6}{8}\left(\frac{e^{4x}}{e}\right)$ = $\frac{6}{8}\left(\frac{e^{4x}}{e^1}\right)$.

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 $e^{}$ for both the parts means base is same.

Here, exponents are different in both parts for one part it is $4x$ and for second part it is 1 and the coefficient is $\frac{6}{8}$.

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

The property of quotient of power states that when dividing two powers with the same base, we subtract the exponents.

Here, is the calculation:

  $\begin{array}{l}\frac{6e^{4x}}{8e^{}}=\frac{6}{8}\left(\frac{e^{4x}}{e}\right)\\ =\frac{6}{8}\left(e^{4x-\left(-1\right)}\right)\\ =\frac{3}{4}\left(e^{4x+1}\right)\end{array}$

The final answer is $\frac{3}{4}\left(e^{4x+1}\right)$.