Question

if a/b=(-3/7)⁹÷(-3/7)⁸,the value of (a/b)³ is​

Answer 1

Given,

$\[\frac{a}{b} = {\left( {\frac{{ - 3}}{7}} \right)^9} \div {\left( {\frac{{ - 3}}{7}} \right)^8}\]$

Solution,

Calculate the value of $\[\frac{a}{b}\]$.

$\[\frac{a}{b} = {\left( {\frac{{ - 3}}{7}} \right)^9} \div {\left( {\frac{{ - 3}}{7}} \right)^8}\]$

$\[ \Rightarrow \frac{a}{b} = {\left( {\frac{{ - 3}}{7}} \right)^9} \times {\left( {\frac{7}{{ - 3}}} \right)^8}\]$

$\[ \Rightarrow \frac{a}{b} = \left( {\frac{{ - 3}}{7}} \right)\]$

Calculate the value of $\[{\left( {\frac{a}{b}} \right)^3}\]$.

$\[ = {\left( {\frac{a}{b}} \right)^3}\]$

$\[ = {\left( {\frac{{ - 3}}{7}} \right)^3}\]$

$\[ = \frac{{ - 27}}{{343}}\]$

Hence the value is $\[ \frac{{ - 27}}{{343}}\]$