Question

Simplify the following expression.

$(c^{-2}{)}^{2/3}\times c^{3/2}÷c^{-3}$ is equal to $c^{\frac{p}{q}}$ . If p snd q are co prime fiind the value of $p+q$.

Answer 1

We have,

${\left(c^{-2}\right)}^{2/3}\times c^{3/2}÷c^{-3}=c^{\frac{p}{q}}$

$c^{-4/3}\times c^{3/2}\times c^3=c^{\frac{p}{q}}$

$c^{-4/3}\times c^{9/2}=c^{\frac{p}{q}}$

$c^{(27-8)/6}=c^{\frac{p}{q}}$

$c^{\frac{19}{6}}=c^{\frac{p}{q}}$

$\therefore p=19,q=6$

So, $p+q=19+6=25$

Hence, this is the answer.