Chapter 4.3, Problem 3E

Solution

To calculate: The value of $e^3·e^4$.

The solution of the given problem is $e^7$.

Given information:

The expression: $e^3·e^4$.

Calculation:

Step 1: Write the problem in two parts.

Take the expression $e^3·e^4$ as $\left(e^3\right)\left(e^4\right)$ and $e^7$

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 3 and for second part it is 4.

The coefficient in each case is number one.

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, add the exponents as follow

  $\begin{array}{c}{e}^3·e^4=e^{(3+4)}\\ =e^7\end{array}$

Step 4: Multiply the coefficients together:

  $\begin{array}{c}{e}^3·e^4=\left(1\times 1\right)e^7\\ =e^7\end{array}$

The required value is $e^7$.