Question

How do you simplify $\dfrac{{4{x^3}}}{{28{x^4}}}$.

Answer 1

Hint: The given question is of algebra and also a part of the question is about indices . We will first solve the numerical part of the given question . Then we will use the standard laws of indices to solve the part of the question where power of a number is used. The formula that will be used for the solution of indices in this question is given by ,
$\dfrac{{{a^x}}}{{{a^y}}} = {a^{x - y}}$

Complete step-by-step solution:
The given question will be solved by first solving the numerical part of the question and then proceeding to solve the remaining part of the question with the indices by using a standard formula for solving index in fraction which is given by :
$\Rightarrow \dfrac{{{a^x}}}{{{a^y}}} = {a^{x - y}}$
The first part goes as follows,
$\Rightarrow \dfrac{{4{x^3}}}{{28{x^4}}}$
Dividing $4$by the numerical part of the denominator we get ,
$\Rightarrow \dfrac{{{x^3}}}{{7{x^4}}}$
Which then comes on to solve the index part, we then write it as,
$\Rightarrow \dfrac{{{x^{(3 - 4)}}}}{7}$
Which on solving the subtraction becomes
$\Rightarrow \dfrac{{{x^{ - 1}}}}{7}$
Which can then be written elegantly as ,
$\Rightarrow \dfrac{1}{{7x}}$

Thus the correct answer is $\dfrac{1}{{7x}}$

Note: Remember these two formulas,
Whenever two expression with the same base but different index are written in a fraction or are divided by each other in a question we use the formula given by,
$\dfrac{{{a^x}}}{{{a^y}}} = {a^{x - y}}$
Similarly whenever two expression with same base but different index are multiplied we can write the formula for this type of expression as :
${a^x}{a^y} = {a^{x + y}}$.