Whakaoti i te (w^3)^8*(w^5)^5

$$( w ^ { 3 } ) ^ { 8 } \cdot ( w ^ { 5 } ) ^ { 5 }$$

Aromātai

$$w^{49}$$

Ngā Upane mō te Hua o ngā Pānga Taupū e Rua

Whakamahia ngā ture taupū hei whakarūnā i te kīanga.

$$\left(w^{3}\right)^{8}\left(w^{5}\right)^{5}$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū.

$$w^{3\times 8}w^{5\times 5}$$

Whakareatia 3 ki te 8.

$$w^{24}w^{5\times 5}$$

Whakareatia 5 ki te 5.

$$w^{24}w^{25}$$

Hei whakarea pū o te pūtake ōrite, tāpiri ana taupū.

$$w^{24+25}$$

Tāpirihia ngā taupū 24 me 25.

$$w^{49}$$

Kimi Pārōnaki e ai ki w

$$49w^{48}$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Pārōnaki

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 3 me te 8 kia riro ai te 24.

$$\frac{\mathrm{d}}{\mathrm{d}w}(w^{24}\left(w^{5}\right)^{5})$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 5 me te 5 kia riro ai te 25.

$$\frac{\mathrm{d}}{\mathrm{d}w}(w^{24}w^{25})$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 24 me te 25 kia riro ai te 49.

$$\frac{\mathrm{d}}{\mathrm{d}w}(w^{49})$$

Ko te pārōnaki o ax^{n} ko nax^{n-1}.

$$49w^{49-1}$$

Tango 1 mai i 49.

$$49w^{48}$$