Question

How do you simplify \[\dfrac{1}{{{x}^{-2}}}\]?

Answer 1

Hint: From the question given, we have been asked to simplify \[\dfrac{1}{{{x}^{-2}}}\]. We can clearly see that the given question is in fraction form and the denominator in it is exponential form containing the negative exponent. We can simplify the given question by using the basic formula and basic laws of exponents. Using the basic laws and basic formulae of exponents we can simplify the given question very easily.

Complete step by step answer:
From the question given, we have been given that \[\dfrac{1}{{{x}^{-2}}}\]
As we have already discussed above, to simplify the given question we have to use the basic formulae of exponents.
The formula we have to use for this question to be solved is shown below: \[{{a}^{-m}}=\dfrac{1}{{{a}^{m}}}\]
By using the above basic formula of exponents, we can solve the given question.
From the question, it has been given that \[\dfrac{1}{{{x}^{-2}}}\]
Now apply the above shown formula to it. By applying the above shown formula to it, we get \[\Rightarrow \dfrac{1}{{{x}^{-2}}}=\dfrac{1}{\dfrac{1}{{{x}^{2}}}}\]
Simplify furthermore the above equation to get the perfect answer.
By simplifying the above equation furthermore, we get \[\Rightarrow \dfrac{1}{{{x}^{-2}}}={{x}^{2}}\]
Hence, the given question is simplified.
As we have already discussed earlier, we solved the given question by using some simple basic formula of exponents.

Note:
We should be very careful while applying the basic formula of exponents to the given question. Also, we should do the calculation without a mistake after applying the basic formula of exponents. Also, we should be well aware of the formulae of exponents and also be well aware of how and when to use the formulae correctly. Similar we have many exponential formulae given as ${{a}^{x}}{{a}^{y}}={{a}^{x+y}}$ , $\dfrac{{{a}^{x}}}{{{a}^{y}}}={{a}^{x-y}}$ , ${{\left( ab \right)}^{x}}={{a}^{x}}{{b}^{x}}$, $\dfrac{{{a}^{x}}}{{{b}^{x}}}={{\left( \dfrac{a}{b} \right)}^{x}}$ and many more.