Question

How do you simplify: \[7{{x}^{-2}}\]?

Answer 1

Hint: Assume the given expression as ‘E’. Now, convert the given expression into the form such that it contains a positive exponent of the term x. Leave the constant term 7 as it is and use the formula: - \[{{a}^{-m}}=\dfrac{1}{{{a}^{m}}}\] for the simplification of the variable x to get the answer.

Complete step by step solution:
Here, we have been provided with the expression \[7{{x}^{-2}}\] and we are asked to simplify it. We are going to use some basic formulas of the topic ‘exponents and powers’. Now, let us assume the given expression as ‘E’. So, we have,
\[\Rightarrow E=7{{x}^{-2}}\]
Now, as we can see that the exponent of the term x is negative, so to simplify this expression means we have to make this exponent of x positive. Here, the constant terms 7 can be written as: $7={{7}^{1}}$, we can see that the exponent of 7 is 1 which is already positive, so here we need to change the form of ${{x}^{-2}}$ to get the answer. Therefore, using the formula: \[{{a}^{-m}}=\dfrac{1}{{{a}^{m}}}\], we get,
\[\begin{align}
  & \Rightarrow E=7\times \dfrac{1}{{{x}^{2}}} \\
 & \Rightarrow E=\dfrac{7}{{{x}^{2}}} \\
\end{align}\]
Hence, the above expression represents the simplified form of the given exponential expression.

Note: One may note that here we have used some basic formulas of the topic ‘exponents and powers’ to solve the question. You must remember all the basic formulas such as: - \[{{a}^{m}}\times {{b}^{n}}={{a}^{m+n}}\], \[{{a}^{m}}\div {{a}^{n}}={{a}^{m-n}}\], \[{{\left( {{a}^{m}} \right)}^{n}}={{a}^{m\times n}}\] and \[{{a}^{-m}}=\dfrac{1}{{{a}^{m}}}\] because they are used everywhere. Here, we cannot simplify the expression further because there is nothing more we can do with it.