Chapter 4.3, Problem 10E

Solution

To calculate: The value of $e^x·5e^{x+3}$.

The value of $e^x·5e^{x+3}$ is $5e^{2x+3}$.

Given information:

Expression: $e^x·5e^{x+3}$.

Calculation:

Solve this problem in steps.

Step 1: Write the problem in simplified form.

The simplified form is $5e^x·e^{x+3}$

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 $x$ and for second part it is $x+3$.

The coefficient is 5.

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

The property of product of power states that when multiplying two powers with the same base, we add the exponents.

Here, is the calculation:

  $\begin{array}{l}{e}^x·5e^{x+3}=5e^x·e^{x+3}\\ =5e^{x+x+3}\\ =5e^{2x+3}\end{array}$

The final answer is $5e^{2x+3}$.