Question

How do you simplify $\dfrac{x}{{{{\left( {2{x^0}} \right)}^2}}}$ and write it using only positive exponents?

Answer 1

Hint: As the rule is that any number raised to the power of 0 equal to 1. Apply this rule in the denominator of the expression. After applying the multiplicative identity property of 1, any number multiplied by 1, gives the same result as the number itself. Then square the terms of the denominator to get the desired result.

Complete step-by-step answer:
The given expression is $\dfrac{x}{{{{\left( {2{x^0}} \right)}^2}}}$.
Let us first understand what simplification is,
Simplification is the process of replacing a mathematical expression with an equivalent one, that is simpler (usually shorter). For example, Simplification of a fraction to an irreducible fraction.
We know that any number raised to the power of 0 equal to 1.
Apply this rule in the denominator of the expression. So, the expression will be,
$ \Rightarrow \dfrac{x}{{{{\left( {2 \times 1} \right)}^2}}}$
Now, the multiplicative identity property of 1 which is any number multiplied by 1, gives the same result as the number itself.
Apply this property in the denominator of the expression. So, the expression will be,
$ \Rightarrow \dfrac{x}{{{{\left( 2 \right)}^2}}}$
Then, square the term in the denominator,
$ \Rightarrow \dfrac{x}{4}$
There are no common factors between the numerator, $x$, and the denominator, 4, so the answer is just
$\therefore \dfrac{x}{4}$

Hence, the simplified expression of $\dfrac{x}{{{{\left( {2{x^0}} \right)}^2}}}$ is $\dfrac{x}{4}$

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 according to the rule of BODMAS where,
B = Bracket
O = of
D = Division
M = Multiplication
A = Addition
S = Subtraction