For positive integers p and q, with \(\frac{p}{q}\ne 1\),…

GATE · 2024 · BM · General AptitudeGATE · 2024 · CE · Set 1 · General AptitudeGATE · 2024 · CH · General AptitudeGATE · 2024 · EY · General AptitudeGATE · 2024 · GG · General AptitudeGATE · 2024 · XH · General Aptitude

For positive integers p and q, with pq≠1\frac{p}{q}\ne 1, (pq)pq=p(pq−1)\left(\frac{p}{q}\right)^{\frac{p}{q}}=p^{\left(\frac{p}{q}-1\right)}. Then,

  1. A.

    qp=pqq^p=p^q

  2. B.

    qp=p2qq^p=p^{2q}

  3. C.

    q=p\sqrt{q}=\sqrt{p}

  4. D.

    qp=pq\sqrt[p]{q}=\sqrt[q]{p}

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