Question

How do you simplify $\left( {2{x^3}} \right)\left( {3{x^4}} \right)$ ?

Answer 1

Hint : In order to simplify the given value, first open the brackets, separate the constants and the variables, then by using simple multiplication multiply the constants and then using law of radicals, find the product of the variables.

Complete step-by-step answer :
We are given with two brackets consisting of variables and constants and that is $\left( {2{x^3}} \right)\left( {3{x^4}} \right)$ .
To simplify the given value, first open the brackets, and we get:
$2 \times {x^3} \times 3 \times {x^4}$
Next separate the variables and the constants together:
$2 \times 3 \times {x^3} \times {x^4}$
Since, we can multiply the constants directly, so multiplying the constants we get:
$6 \times {x^3} \times {x^4}$
For the variables, we would be using the Law of radicals, according to which the powers will be added if the values have a common base during multiplication and the result will be stored in one of the common base and simplifying using this property, we get:
$6 \times {x^3} \times {x^4} = 6 \times {x^{3 + 4}} = 6 \times {x^7} = 6{x^7}$
Hence, after simplifying the value $\left( {2{x^3}} \right)\left( {3{x^4}} \right)$ , we get $6{x^7}$ .
So, the correct answer is “ $6{x^7}$ ”.

Note : Law of radicals:
I.When the base would be the same during multiplication then the powers would be added to the variables and would be stored in any one variable present. For ex: ${p^a}.{p^b} = {p^{a + b}}$
II.When the base would be the same during division of variables, then powers would be subtracted. For Ex: $\dfrac{{{p^a}}}{{{p^b}}} = {p^{a - b}}$