Question

How do you simplify $ {\left( {\dfrac{2}{3}} \right)^{ - 1}} $ ?

Answer 1

Hint: In order to solve $ {\left( {\dfrac{2}{3}} \right)^{ - 1}} $ , first remove the negative power by comparing it to the formula we know, that is $ {\left( x \right)^{ - 1}} = \dfrac{1}{x} $ , after this we know that if the denominator of a fraction is also a fraction then multiply the numerator and denominator of the main fraction with the value of denominator of denominator to make it a simple fraction. So, did with the same method for our question given.

Complete step by step solution:
 We are given with $ {\left( {\dfrac{2}{3}} \right)^{ - 1}} $ , we need to first remove the negative power.
 Comparing the value with the formula known that is $ {\left( x \right)^{ - 1}} = \dfrac{1}{x} $ , we get:
 $ {\left( {\dfrac{2}{3}} \right)^{ - 1}} = \dfrac{1}{{\left( {\dfrac{2}{3}} \right)}} $
Since, the denominator of the denominator is given as $ 3 $ , so multiply the numerator and denominator by $ 3 $ and we get:
 $\Rightarrow \dfrac{1}{{\left( {\dfrac{2}{3}} \right)}} = \dfrac{{1 \times 3}}{{\left( {\dfrac{2}{3}} \right) \times 3}} = \dfrac{3}{2} $
As we can see that $ 3 $ got cancelled from the denominator and we are left with the simplest fraction and this is the result we obtained.
Hence, $ {\left( {\dfrac{2}{3}} \right)^{ - 1}} $ is simplified and can be written as $ \left( {\dfrac{3}{2}} \right) $ .
So, the correct answer is “ $ \left( {\dfrac{3}{2}} \right) $ .”.

Note: Always cross check the answers for confirmation.
Solve step by step with the help of formula rather than trying it to solve at once. For small questions this may be easy but for lengthy questions, it becomes difficult to solve at once, and increases the chances of giving an error.
If the power is negative then only these steps are followed otherwise if the powers are in fractions, or decimal form then simply expand the value accordingly. For example:
 $ {\left( {\dfrac{2}{3}} \right)^3} = \left( {\dfrac{2}{3}} \right) \times \left( {\dfrac{2}{3}} \right) \times \left( {\dfrac{2}{3}} \right) = \dfrac{8}{{27}} $ In this Question the power was not negative then was no need to write it in the denominator and going with the above steps, just simplified it.