Question

How do you simplify $ {\left( { - \dfrac{3}{4}c} \right)^3} $ ?

Answer 1

Hint: To simplify this question , we need to solve it step by step . starting form the parentheses with exponent over it , this means that the rational number $ - \dfrac{3}{4}c $ ( the number which can be expressed as in the form of $ \dfrac{p}{q} $ , where p is numerator and q is denominator also q $ \ne $ 0 . ) is having cube over the numerator and the denominator also . We should first write the cube of 3 also ‘ c ’ in the numerator and then the cube of 4 in the denominator . Then simplify it to get the desired answer .

Complete step-by-step answer:
The rational number with whole exponent as cube can be expressed as the number with no exponent by writing their respective cube that is for any fraction
 $ {\left( {\dfrac{p}{q}} \right)^n} = \dfrac{{{p^n}}}{{{q^n}}} $ , p is numerator and q is denominator and n is the exponent which is distributed over the numerator and denominator .
\[{\left( { - \dfrac{3}{4}} \right)^3} = \left( { - \dfrac{3}{4}c} \right) \cdot \left( { - \dfrac{3}{4}c} \right) \cdot \left( { - \dfrac{3}{4}c} \right) = - \dfrac{{3 \cdot 3 \cdot 3}}{{4 \cdot 4 \cdot 4}} \bullet c \bullet c \bullet c = - \dfrac{{{3^3}}}{{{4^3}}} \bullet {c^3}\] .
 So , calculating the cube of the respective numbers= \[{\left( { - \dfrac{3}{4}c} \right)^3}\]= \[ - \dfrac{{{3^3}}}{{{4^3}}} \bullet {c^3}\]= $ - \dfrac{{27}}{{64}}{c^3} $
Now , In order to solve the fraction into its simplified form =>
To simplify the fraction we need to find the Greatest Common Divisor of numerator and denominator of the fraction $ - \dfrac{{27}}{{64}}{c^3} $ .
The Greatest Common Divisor of 343 and 64 is 1 . Then divide the numerator and denominator by the Greatest Common Divisor .
 $ \dfrac{{27 \div 1}}{{64 \div 1}} $ = $ \dfrac{{27}}{{64}} $ .
Therefore , the reduced fraction is $ - \dfrac{{27}}{{64}}{c^3} $ $ $ . It is already in its simplest form.
So, the correct answer is “ $ - \dfrac{{27}}{{64}}{c^3} $ $ $ ”.

Note: You should always remember that the square of -1 or any negative number will become positive .
But the cube of the negative number will always remain negative .
Greatest common factor itself describes the number which has in common factor , there is only one common factor 1 of 27 and 64 .