Chapter 4.3, Problem 2GP

Solution

To calculate: The value of the expression $2e^{-3}.6e^5$.

The required is $12e^2$.

Given information:

The expression $2e^{-3}.6e^5$.

Calculation:

Let’s solve this problem in steps.

Step 1: Write the problem in two parts

Take the expression $2e^{-3}.6e^5$ as $\left(2e^{-3}\right)\left(6e^5\right)$

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 -3 and for second part it is 5.

Here coefficient for first part is 2 and for second part it is 6.

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 while calculating:

  $e^{(-3+5)}=e^2$

Step 4:

Multiply the coefficients together:

  $\left(2\times 6\right)e^2=12e^2$

Hence, required value is $12e^2$.