Question

How do you simplify \[{\left( {\dfrac{5}{6}} \right)^2}\]?

Answer 1

Hint:
In the given question, we have been given a fraction. The fraction is raised to some integral power. We have to calculate the value of the fraction raised to that power. We can easily do that by just simply multiplying the fraction by itself as many times as is the value of the power.

Formula Used:
In this question, we are going to use the formula of square, which is:
\[{a^2} = a \times a\]

Complete step by step answer:
The given fraction in the question is \[{\left( {\dfrac{5}{6}} \right)^2}\].
So, this fraction is going to be multiplied with itself twice, hence,
\[{\left( {\dfrac{5}{6}} \right)^2} = \dfrac{5}{6} \times \dfrac{5}{6} = \dfrac{{25}}{{36}}\]

Additional Information:
In this question, the power is positive. But, if it was negative, then we would have first converted it to a positive power by taking the reciprocal of the fraction and then approaching as normal, or,
\[{\left( {\dfrac{a}{b}} \right)^{ - n}} = {\left( {\dfrac{b}{a}} \right)^n}\]

Note:
So, for solving questions of such type, we first write what has been given to us. Then we write down what we have to find. Then we write the formula which connects the two things. In the question, there was a proper fraction which was squared. We multiplied it twice because the power on its head (two) means that the number is supposed to be multiplied with itself twice. If there was any other power, then we would have multiplied the fraction with itself that many times.