Question

a power p-q x a power q-r= 1​

Answer 1

${a}^{p - q} \times {a}^{q - r} = 1$

$= > {a}^{p - q} \times {a}^{q - r} = {a}^{0}$

$= > p - q + q - r = 0$

$= > p - r = 0$

$= > p = r$

Laws used:

1. ${x}^{a} \times {x}^{b} = {x}^{a + b}$
2. ${x}^{0} = 1$
3. When bases are same powers are equated.

Hope it helps !