GATE Chemical 2024 | GA | Question: 3

Question

For positive integers $p$ and $q$, with $\frac{p}{q} \neq 1,\left(\frac{p}{q}\right)^{\frac{p}{q}}=p^{\left(\frac{p}{q}-1\right)}$. Then,

• A. $q^{p}=p^{q}$
• B. $q^{p}=p^{2 q}$
• C. $\sqrt{q}=\sqrt{p}$
• D. $\sqrt[p]{q}=\sqrt[q]{p}$

 

Answer 1

(p/q)^(p/q)  = p^{(p/q -1)}

(p^p/q) /(q^p/q) = p^{(p/q -1)}

(p^p/q) = p^{(p/q -1) *} (q^p/q)

(p^p/q) = p^{(p/q )*}p^{( -1) *} (q^p/q)

p^{( 1)  =}  (q^p/q)

p^{( 1) *q  =}  (q^p/q)*^q

p^{q  =} q^p