Question

If x^p^q = (x^√p)^q. Find p in terms of q.

Answer 1

Answer:

$p=q^{\frac{2}{2q-1}}$

Step-by-step explanation:

Given:

$x^{p^q}=(x^{\sqrt{p}})^q$

$x^{p^q}=x^{q{\sqrt{p}}}$

Equating powers on both sides, we get

$p^q=q\sqrt{p}$

$p^q=q{p^\frac{1}{2}}$

$\frac{p^q}{p^\frac{1}{2}}=q$

$p^q.p^\frac{-1}{2}=q$

$p^{q-\frac{1}{2}}=q$

$p^{\frac{2q-1}{2}}=q$

Raising both sides to the power $\frac{2}{2q-1}$

$p=q^{\frac{2}{2q-1}}$