Question

If ${\left(\frac{a}{b}\right)}^2=\left(\frac{16}{9}\right)÷{\left(\frac{4}{3}\right)}^0$ find the value of ${\left(\frac{b}{a}\right)}^3$.

Answer 1

${\left(\frac{a}{b}\right)}^2=\frac{16}{9}÷{\left(\frac{4}{3}\right)}^0$

$\Rightarrow {\left(\frac{a}{b}\right)}^2=\frac{16}{9}÷1$

$\Rightarrow {\left(\frac{a}{b}\right)}^2=\frac{16}{9}$

$\Rightarrow \frac{a}{b}={\left({\left(\frac{4}{3}\right)}^2\right)}^{\frac{1}{2}}$

$\Rightarrow \frac{a}{b}=\frac{4}{3}$

$\Rightarrow \frac{b}{a}=\frac{3}{4}$

$\therefore {\left(\frac{b}{a}\right)}^3={\left(\frac{3}{4}\right)}^3=\frac{27}{64}$