Question

How do you simplify $\dfrac{{{x^7}}}{{{x^5}}}?$

Answer 1

Hint: for solving such types of questions we will use some basic formulas of mathematics. Here in these questions denominator and numerator have the same value, only the power of them is different. so we need to check four possible combinations we can have and after checking we will use formulas and directly get the answer.

Formula used:
you should know this formulas to solve such type of question:
$
   \Rightarrow \dfrac{{{x^a}}}{{{x^b}}} = {x^{a - b}} \\
   \Rightarrow \dfrac{{{x^{ - a}}}}{{{x^b}}} = {x^{ - a - b}} \\
   \Rightarrow \dfrac{{{x^a}}}{{{x^{ - b}}}} = {x^{a + b}} \\
   \Rightarrow \dfrac{{{x^{ - a}}}}{{{x^{ - b}}}} = {x^{ - a + b}} \\
   \Rightarrow {x^a} \times {x^b} = {x^{a + b}} \\
   \Rightarrow {x^a} \times {x^{ - b}} = {x^{a - b}} \\
   \Rightarrow {x^{ - a}} \times {x^b} = {x^{ - a + b}} \\
   \Rightarrow {x^{ - a}} \times {x^{ - b}} = {x^{ - a - b}} \\
$

Complete step by step solution:
Here, for solving these question we will use
$ \Rightarrow \dfrac{{{x^a}}}{{{x^b}}} = {x^{a - b}}$
Now the value of a is $7$ and value of b is $5$. So after substituting the values of a and b into the equation we get,
$ \Rightarrow \dfrac{{{x^7}}}{{{x^5}}} = {x^{7 - 5}} = {x^2}$

Right answer to this question is ${x^2}$.

Note:
As you have seen, try to solve maximum numbers of these types of questions. When you practice many questions of these types you will be able to solve these types of questions within a minute. These will benefit you for understanding high grade mathematics problems. so try to solve these questions exacting denominator’s power and numerator’s power.