45) q²⁰ⁿ: q⁰ q¹³ⁿ:q⁸ⁿ·q¹¹ⁿ =

45) $$ \frac{q^{20n}: q^0}{q^{13n}:q^{8n} \cdot q^{11n}} = \frac{q^{20n-0}}{q^{13n}:q^{8n+11n}} = \frac{q^{20n}}{q^{13n}:q^{19n}} = \frac{q^{20n}}{q^{13n-19n}} = \frac{q^{20n}}{q^{-6n}} = q^{20n-(-6n)} = q^{20n+6n} = q^{26n}$$

Ответ: q²⁶ⁿ