Question

How do you rewrite the expression $ \dfrac{{{x^2}}}{{{y^3}}} $ without fractions?

Answer 1

Hint: We have to eliminate the fraction in this question. We will do this by getting the reciprocal of the denominator of this given fraction. Since the reciprocal will convert the whole fraction to one type which in this case is the numerator and we will thus have to eliminate the fractions from the given question. We have to find the reciprocal of the denominator but since our denominator contains an index (also called exponent) we will have to use the law of indices in doing the reciprocal. The identity which we will have to use is the identity that will change the positive index to the negative index and also do the reciprocal. The identity is given below,
 $ {a^y} = \dfrac{1}{{{a^{ - y}}}} $
This we will apply on the denominator and get our answer in the numerator.

Complete step by step solution:
The given question asks us to convert the given number into a number without a fraction. We will use the law for taking reciprocal of positive index and changing it into a negative index. The formula we will use is
 $ {a^y} = \dfrac{1}{{{a^{ - y}}}} $
Our question will become,
 $ \dfrac{{{x^2}}}{{{y^3}}} = {x^2} \times {y^{ - 3}} $
We will then elegantly write our answer as,
 $ {x^2}{y^{ - 3}} $
Which is the required answer.
So, the correct answer is “ $ {x^2}{y^{ - 3}} $ ”.

Note: We should always remember that whenever we have a positive power we can easily convert it into negative power but it will also render the reciprocal of the number instead of the original number this specific law of exponent is written in the below written formula,
 $ {a^y} = \dfrac{1}{{{a^{ - y}}}} $