Question

The simplified value of $(5^{-1}÷4^{-1}{)}^3$ is given by $\frac{a}{b}$, where $a$ and $b$ are co-primes, then find the value of $2a-b$.

Answer 1

$(5^{-1}÷4^{-1}{)}^3$
$={(\frac{1}{5}÷\frac{1}{4})}^3$
$={\left(\frac{4}{5}\right)}^3$
$=\frac{64}{125}$

Hence, $a=64$ and $b=125$

$\therefore 2a-b=2\times 64-125=128-125=3$