Whakaoti i te (x^10)^-7/x^9

$$\frac { ( x ^ { 10 } ) ^ { - 7 } } { x ^ { 9 } }$$

Aromātai

$$\frac{1}{x^{79}}$$

Ngā Upane mō te Hua o ngā Pānga Taupū e Rua

Whakamahia ngā ture taupū hei whakarūnā i te kīanga.

$$\left(x^{10}\right)^{-7}\times \frac{1}{x^{9}}$$

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

$$x^{10\left(-7\right)}x^{9\left(-1\right)}$$

Whakareatia 10 ki te -7.

$$x^{-70}x^{9\left(-1\right)}$$

Whakareatia 9 ki te -1.

$$x^{-70}x^{-9}$$

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

$$x^{-70-9}$$

Tāpirihia ngā taupū -70 me -9.

$$x^{-79}$$

Kimi Pārōnaki e ai ki x

$$-\frac{79}{x^{80}}$$

Ngā Upane e Whakamahi ana i te Ture Mekameka

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 10 me te -7 kia riro ai te -70.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{-70}}{x^{9}})$$

Tuhia anō te x^{9} hei x^{-70}x^{79}. Me whakakore tahi te x^{-70} i te taurunga me te tauraro.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x^{79}})$$

Mēnā ko F te hanganga o ngā pānga e rua e taea ana te pārōnaki f\left(u\right) me u=g\left(x\right), arā, mēnā ko F\left(x\right)=f\left(g\left(x\right)\right), ko te pārōnaki o F te pārōnaki o f e ai ki u whakareatia te pārōnaki o g e ai ki x, arā, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

$$-\left(x^{79}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{79})$$

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}.

$$-\left(x^{79}\right)^{-2}\times 79x^{79-1}$$

Whakarūnātia.

$$-79x^{78}\left(x^{79}\right)^{-2}$$