Question

How do you simplify $\left( {5{x^3}} \right){\left( {2x} \right)^{ - 3}}$?

Answer 1

Hint: In this question, we will use the basic concept of algebra. We can apply operations like converting negative powers into positive. First, convert the negative power by moving the term in the denominator. After that cube the term in the denominator. Then cancel out the common factor to get the desired result.

Complete step-by-step answer:
We have been given an expression $\left( {5{x^3}} \right){\left( {2x} \right)^{ - 3}}$.
An algebraic expression is a combination of constants, variables, and operators. The four basic operations of mathematics are addition, subtraction, multiplication, and division can be performed on algebraic expressions. The addition and subtraction of algebraic expressions are quite similar to the addition and subtraction of numbers. However, when it comes to the algebraic expressions, you must sort the like terms and the unlike terms together. In this article, we will learn about the addition and subtraction of algebraic expressions, how to sort the like and unlike terms, and have a look at some of the solved examples.
First, convert the negative power into positive by moving the term in denominator,
$ \Rightarrow \left( {5{x^3}} \right) \times \dfrac{1}{{{{\left( {2x} \right)}^3}}}$
Now cube the term of the bracket in the denominator,
$ \Rightarrow 5{x^3} \times \dfrac{1}{{8{x^3}}}$
Then, cancel out the common factor from numerator and denominator,
$ \Rightarrow \dfrac{5}{8}$

Hence, the simplification of $\left( {5{x^3}} \right){\left( {2x} \right)^{ - 3}}$ is $\dfrac{5}{8}$.

Note:
You should have an idea of BODMAS which is used to simplify the mathematical expression involving different mathematical operators. The different operators are used in according the rule of BODMAS where,
B = Bracket
O = Of
D = Division
M = Multiplication
A = Addition
S = Subtraction