Question

How do you simplify ${\left( {\dfrac{7}{4}} \right)^3}$?

Answer 1

To simplify this question , we need to solve it step by step . starting from the parentheses with exponent over it , this means that the rational number $\dfrac{7}{4}$ ( 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 7 in the numerator and then the cube of 3 in the denominator . Then simplify it to get the desired answer .

Complete Step by step Solution :
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 .

\cdot 7 \cdot 7}}{{4 \cdot 4 \cdot 4}} = \dfrac{{{7^3}}}{{{4^3}}}$$ . So , calculating the cube of the respective numbers= $${\left( {\dfrac{7}{4}} \right)^3}$$= $$\dfrac{{{7^3}}}{{{4^3}}}$$= $\dfrac{{343}}{{64}}$ Now , In order to solve the fraction into its simplified form => To simplify the fraction we need to find the Greatest Common Divisor of numerator and denominator of the fraction $\dfrac{{343}}{{64}}$ . The Greatest Common Divisor of 343 and 64 is 1 . Then divide the numerator and denominator by the Greatest Common Divisor . $\dfrac{{343 \div 1}}{{64 \div 1}}$=$\dfrac{{343}}{{64}}$ . **Therefore , the reduced fraction is $\dfrac{{343}}{{64}}$. It is already in its simplest form . It can be written as $$5.359375$$in the decimal form .** **Note:** 1\. Rational number is a number which is expressed in the form of $\dfrac{p}{q}$where $q \ne 0$. 2.Do the calculation properly . 3.Make sure to write the fraction into its simplest form at the end of the result.