Chapter 4.3, Problem 18E

Solution

To calculate: The error in simplifying the given problem.

The error is that powers are added here while the property of quotient says when same bases are divided their exponents are subtracted. The correct answer for the given expression is $e^{8x}$.

Given information:

Simplifying of the problem,

  $\begin{array}{l}\frac{e^{6x}}{e^{-2x}}=e^{6x-2x}\\ =e^{4x}\end{array}$.

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

Here, property of quotient goes which says when same bases are divided their exponents are subtracted.

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 $e^{}$.

  $\begin{array}{l}\frac{e^{6x}}{e^{-2x}}=e^{6x-\left(-2x\right)}\\ =e^{8x}\end{array}$

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