Whakaoti i te 4x^2/4x^7

$$\frac { 4 x ^ { 2 } } { 4 x ^ { 7 } }$$

Aromātai

$$\frac{1}{x^{5}}$$

Ngā Upane mō te Hua o ngā Pānga Taupū e Rua

Whakamahia ngā ture taupū hei whakarūnā i te kīanga.

$$\left(4x^{2}\right)^{1}\times \frac{1}{4x^{7}}$$

Hei hiki i te hua o ngā tau e rua, neke atu rānei ki tētahi pū, hīkina ia tau ki te pū ka tuhi ko tāna hua.

$$4^{1}\left(x^{2}\right)^{1}\times \frac{1}{4}\times \frac{1}{x^{7}}$$

Whakamahia te Āhuatanga Kōaro o te Whakareanga.

$$4^{1}\times \frac{1}{4}\left(x^{2}\right)^{1}\times \frac{1}{x^{7}}$$

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

$$4^{1}\times \frac{1}{4}x^{2}x^{7\left(-1\right)}$$

Whakareatia 7 ki te -1.

$$4^{1}\times \frac{1}{4}x^{2}x^{-7}$$

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

$$4^{1}\times \frac{1}{4}x^{2-7}$$

Tāpirihia ngā taupū 2 me -7.

$$4^{1}\times \frac{1}{4}x^{-5}$$

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

$$4^{1-1}x^{-5}$$

Tāpirihia ngā taupū 1 me -1.

$$4^{0}x^{-5}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$1x^{-5}$$

Mō tētahi kupu t, t\times 1=t me 1t=t.

$$x^{-5}$$

Ngā Upane mō te Otinga o ngā Pānga Taupū

Whakamahia ngā ture taupū hei whakarūnā i te kīanga.

$$\frac{4^{1}x^{2}}{4^{1}x^{7}}$$

Hei whakawehe i ngā pū o te pūtake kotahi, tangohia te taupū o te tauraro mai i te taupū o te taurunga.

$$4^{1-1}x^{2-7}$$

Tango 1 mai i 1.

$$4^{0}x^{2-7}$$

Mō tētahi tau a mahue te 0, a^{0}=1.

$$x^{2-7}$$

Tango 7 mai i 2.

$$x^{-5}$$

Kimi Pārōnaki e ai ki x

$$-\frac{5}{x^{6}}$$

Ngā Upane Otinga

Hei whakawehe i ngā pū o te pūtake kotahi, tangohia te taupū o te tauraro mai i te taupū o te taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{4}x^{2-7})$$

Mahia ngā tātaitanga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-5})$$

Ko te pārōnaki o tētahi pūrau ko te tapeke o ngā pārōnaki o ōna kīanga tau. Ko te pārōnaki o tētahi kīanga tau pūmau ko 0. Ko te pārōnaki o te ax^{n} ko te nax^{n-1}.

$$-5x^{-5-1}$$

Mahia ngā tātaitanga.

$$-5x^{-6}$$