Question

How do you simplify $2{{x}^{-2}}$?

Answer 1

Hint:
In this problem we need to simplify the $2{{x}^{-2}}$. In this problem we can observe that inverse algebra. In inverse algebra we have the exponential rule ${{x}^{-a}}=\dfrac{1}{{{x}^{a}}}$. So, we will first simplify the value of ${{x}^{-2}}$ by using the above equation and then we will multiply the obtained equation with $2$ to get the required result.

FORMULA USED:
1. change of sign rule exponent that is
${{x}^{-a}}=\dfrac{1}{{{x}^{a}}}$

Complete step by step solution:
Given that, $2{{x}^{-2}}$
Considering the value of ${{x}^{-2}}$. Comparing this value with ${{x}^{-a}}$, then we will get value of $a$ as
$a=2$
From the change of sign rule, we can write
${{x}^{-a}}=\dfrac{1}{{{x}^{a}}}$
Substituting $a=2$ in the above equation, then we will get
${{x}^{-2}}=\dfrac{1}{{{x}^{2}}}$
Multiplying the above equation with $2$ on both sides of the above equation, then we will get
$2\times {{x}^{-2}}=2\times \dfrac{1}{{{x}^{2}}}$
Simplifying the above equation, then we will get
$\Rightarrow 2{{x}^{-2}}=\dfrac{2}{{{x}^{2}}}$
Hence the final result is

$\therefore 2{{x}^{-2}}=\dfrac{2}{{{x}^{2}}}$

Note:
When dealing with exponential problems it is better to know all the exponential rules and formulas. Generally, we have $9$ exponential rules that we have used very regularly.
Product rule gives that the value of ${{x}^{a}}\times {{x}^{b}}$ as ${{x}^{a+b}}$. Mathematically we can write ${{x}^{a}}{{x}^{b}}={{x}^{a+b}}$.
Quotient rule gives that the value of $\dfrac{{{x}^{a}}}{{{x}^{b}}}$ as ${{x}^{a-b}}$. Mathematically we can write $\dfrac{{{x}^{a}}}{{{x}^{b}}}={{x}^{a-b}}$.
Power of power rule gives that the values of ${{\left( {{x}^{a}} \right)}^{b}}$ as ${{x}^{ab}}$ ${{\left( {{x}^{a}} \right)}^{b}}={{x}^{ab}}$.
Similarly, we have remaining rules and their mathematical representations are given below.
Power of a product rule is ${{\left( xy \right)}^{ab}}={{x}^{a}}{{y}^{b}}$.
Power of one rule is ${{x}^{1}}=x$.
Power of zero rule ${{x}^{0}}=1$.
Power of negative rule is ${{x}^{-a}}=\dfrac{1}{x}$.
Change of sign rule is ${{x}^{-a}}=\dfrac{1}{{{x}^{a}}}$.
Fractional rule is ${{x}^{\dfrac{m}{n}}}=\sqrt[n]{{{x}^{m}}}$.