How do you simplify the expression \[\dfrac{{9x{{10}^{-31}}.{{(3x{{10}^7})}^2}}}{2}\]

Hint: The equation is an algebraic equation, where the algebraic equation is the combination of constants and variables. Here in this question we have to simplify the given algebraic equation, the algebraic equation is in the form of fraction and by using the law of exponents we can solve the given question.

Complete step by step solution:
The algebraic expression is an expression which consists of variables and constants with the arithmetic operations. Since it contains the exponents form we can use the law of exponents for the given algebraic expression ,we apply simple methods. Since by solving these types of expression we get the simplified form.
Now consider the given algebraic expression
 \[\dfrac{{9x{{10}^{-31}}.{{(3x{{10}^7})}^2}}}{2}\]
In the numerator the operation is involved as a multiplication operation, so we multiply the terms and rewrite the algebraic expression.
Before the second term contains a square, so first we find the square.
 \[ \Rightarrow \dfrac{{9x{{10}^{-31}}.(9{x^2}{{10}^{14}})}}{2}\]
First we multiply the numbers we have
  \[ \Rightarrow \dfrac{{81x{x^2}{{10}^{ - 31}}{{10}^{14}}}}{2}\]
By the law of exponents we have \[{a^{m + n}} = {a^m}.{a^n}\] , using this law of exponent the algebraic expression is written as
 \[ \Rightarrow \dfrac{{81{x^{1 + 2}}{{10}^{ - 31 + 14}}}}{2}\]
On simplifying the some terms we have
 \[ \Rightarrow \dfrac{{81{x^3}{{10}^{ - 17}}}}{2}\]
In the term let we take the exponent number which is present in the numerator to the denominator and therefore the algebraic expression is written as
 \[ \Rightarrow \dfrac{{81{x^3}}}{{2 \times {{10}^{17}}}}\]
Hence the algebraic expression is simplified.
So, the correct answer is “ \[ \dfrac{{81{x^3}}}{{2 \times {{10}^{17}}}}\] ”.

Note: The algebraic equation or an expression is a combination of variables and constants, it also contains the coefficient. The alphabets are known as variables. The x, y, z etc., are called as variables. The numerals are known as constants. The numeral of a variable is known as co-efficient. We have 3 types of algebraic expressions namely monomial expression, binomial expression and polynomial expression. By using the law of exponent and simple arithmetic operations, we can solve the equation.