Question

How do you simplify \[\dfrac{{{x}^{8}}}{{{x}^{10}}}\]?

Answer 1

Hint: In this problem, we have to simplify the given fraction. We have numerator and denominator in this problem, in the denominator, we can use the power of product rule to separate it and we can cancel the similar terms in the numerator and the denominator. For these types of problems, we should know the basic power rules, like the power of product rules, to solve them.

Complete step by step answer:
We know that the given fraction to be simplified is,
\[\dfrac{{{x}^{8}}}{{{x}^{10}}}\]
We know that the power of product rule is of the form
\[{{x}^{a+b}}={{x}^{a}}\times {{x}^{b}}\]
From this, we can change the denominator into separate terms in order to simplify using product rules.
We can use the power of product rule in the denominator, we get
\[\Rightarrow \dfrac{{{x}^{8}}}{{{x}^{8}}\times {{x}^{2}}}\text{ }\because {{x}^{8+2}}={{x}^{8}}\times {{x}^{2}}\]
Now, we can cancel the similar terms to get the simplified value of the given problem,
\[\Rightarrow \dfrac{1}{{{x}^{2}}}\]
Now we can take reciprocal of the solution to get the simplified form, we get
\[\Rightarrow {{x}^{-2}}\]
Therefore, the simplified form of \[\dfrac{{{x}^{8}}}{{{x}^{10}}}\] is \[{{x}^{-2}}\] or \[\dfrac{1}{{{x}^{2}}}\].

Note: Students make mistakes in the formula part such as power of product rule and power of quotient rule. Students should know some basic power rules to solve these types of problems. We can separate the power term using power of product rule to our convenience in order to cancel the similar terms in the numerator. We can also write the final answer in fraction form or power form.