Chapter 4.3, Problem 5E

Solution

To calculate: The value of ${(2e^{3x})}^3$.

The solution of the given problem is $8e^{9x}$ .

Given information: Compute the given expression ${(2e^{3x})}^3$ .

Calculation: Step 1: Check which property of exponents goes with the given question.

Here, property of power raised to a power meets which states that if a is a base then the power raised to the power of base a gives the product of powers raised to the base a. it means ${\left(a^m\right)}^n=a^{mn}$

Solve this problem in steps.

Step 2: Write the problem in two parts.

First part $2^3$ and $e^{3x\left(3\right)}$

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 $e^{}$ .

The coefficient is $2^3$ .

  $2^3=8$ And

  $e^{3x\left(3\right)}=e^{9x}$

The final answer for the given expression is $8e^{9x}$ .