Question

How do you simplify \[{\left( { - \dfrac{4}{9}} \right)^2}\] ?

Answer 1

Hint: Here in this question in the form of fraction. First eliminate the square by a multiplying fraction by itself and to simplify a fraction divide the top and bottom i.e., numerator and denominator of the given fraction by the highest common factor. This means look for the biggest number then divide into both, if gives the simplest form of the fraction.

Complete step-by-step answer:
The given question in the form of \[\dfrac{a}{b}\] where, a is the numerator and b is the denominator this form is known as fraction, there are mainly two types of fraction namely
Proper fraction: If the numerator is smaller than the denominator is known as proper fraction.
Improper fraction: If the numerator is greater than or equal to the denominator of a fraction, then it is called an improper fraction. In that case, you could convert it into a whole number or mixed number fraction
Simplification of fraction: To simplify a fraction we divide both the numerator and denominator by the same number. A common factor is a number that divides both the numerator and denominator without leaving any remainders. We divide the fractions till we get 1 as the common factor for both the numerator and denominator.
Consider the given fraction
 \[ \Rightarrow \,\,\,{\left( { - \dfrac{4}{9}} \right)^2}\]
To square a fraction, you multiply the fraction by itself. Another way to think about it is to multiply the numerator by itself and then the denominator by itself and we know the Negative number raised to an even power is positive.
Square of 4 is 16 and 9 is 81 then
 \[ \Rightarrow \,\,\,\dfrac{{16}}{{81}}\]
Hence the above fraction is a proper fraction, where 16 is numerator and 81 is denominator.
Next, to simplify the fraction find the factors of both numerator and denominator.
Factor of 16 is 1, 2, 4, 8 and 16
Factors of 81 is 1, 3, 9, 27 and 81
There is no common factor between 16 and 81.
Hence the simplest form of the given fraction \[{\left( { - \dfrac{4}{9}} \right)^2}\] is \[\dfrac{{16}}{{81}}\] .
So, the correct answer is “ \[\dfrac{{16}}{{81}}\] ”.

Note: The square is multiplying the number by itself twice. When the number is multiplying two times by itself then it is called square or squaring. The sign will also change when we apply the square to it. The plus sign will not change by squaring, but the minus sign will change. The table of multiplication is needed to multiply the numbers.