Alg3.3.10

If $x=a^p,y=a^q\,$ and $x^q\cdot y^p=a^{\frac{2}{r}}\,$ .Show that $pqr=1\,$

Given that $x=a^p,y=a^q\,$ and $x^q\cdot y^p=a^{\frac{z}{r}}\,$ .

Substituting the values of x and y in the given condition $x^q\cdot y^p=a^{\frac{2}{r}}\,$ .

we get

$(a^p)^{q} \cdot (a^q)^{p}=a^{\frac{2}{r}}\,$

$a^{pq} \cdot a^{pq}=a^{\frac{2}{r}}\,$

$a^{2pq}=a^{\frac{2}{r}}\,$

Since the bases on both sides are equal,

$2pq=\frac{2}{r}\,$

Therefore

$pqr=1\,$