Whakaoti i te (81/16)^{025}*((-8)^-frac{4{3}}*a^-8)*(2^-2*a^30)=

$$( \frac { 81 } { 16 } ) ^ { 025 } \cdot ( ( - 8 ) ^ { - \frac { 4 } { 3 } } \cdot a ^ { - 8 } ) \cdot ( 2 ^ { - 2 } \cdot a ^ { 30 } ) =$$

Aromātai

$$\frac{a^{22}}{64}$$

Ngā Upane Otinga

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te -8 me te 30 kia riro ai te 22.

$$\left(\frac{81}{16}\right)^{0\times 25}\left(-8\right)^{-\frac{4}{3}}a^{22}\times 2^{-2}$$

Whakareatia te 0 ki te 25, ka 0.

$$\left(\frac{81}{16}\right)^{0}\left(-8\right)^{-\frac{4}{3}}a^{22}\times 2^{-2}$$

Tātaihia te \frac{81}{16} mā te pū o 0, kia riro ko 1.

$$1\left(-8\right)^{-\frac{4}{3}}a^{22}\times 2^{-2}$$

Tātaihia te -8 mā te pū o -\frac{4}{3}, kia riro ko \frac{1}{16}.

$$1\times \frac{1}{16}a^{22}\times 2^{-2}$$

Whakareatia te 1 ki te \frac{1}{16}, ka \frac{1}{16}.

$$\frac{1}{16}a^{22}\times 2^{-2}$$

Tātaihia te 2 mā te pū o -2, kia riro ko \frac{1}{4}.

$$\frac{1}{16}a^{22}\times \frac{1}{4}$$

Whakareatia te \frac{1}{16} ki te \frac{1}{4}, ka \frac{1}{64}.

$$\frac{1}{64}a^{22}$$

Kimi Pārōnaki e ai ki a

$$\frac{11a^{21}}{32}$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Pārōnaki

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te -8 me te 30 kia riro ai te 22.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(\frac{81}{16}\right)^{0\times 25}\left(-8\right)^{-\frac{4}{3}}a^{22}\times 2^{-2})$$

Whakareatia te 0 ki te 25, ka 0.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(\frac{81}{16}\right)^{0}\left(-8\right)^{-\frac{4}{3}}a^{22}\times 2^{-2})$$

Tātaihia te \frac{81}{16} mā te pū o 0, kia riro ko 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(1\left(-8\right)^{-\frac{4}{3}}a^{22}\times 2^{-2})$$

Tātaihia te -8 mā te pū o -\frac{4}{3}, kia riro ko \frac{1}{16}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(1\times \frac{1}{16}a^{22}\times 2^{-2})$$

Whakareatia te 1 ki te \frac{1}{16}, ka \frac{1}{16}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{16}a^{22}\times 2^{-2})$$

Tātaihia te 2 mā te pū o -2, kia riro ko \frac{1}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{16}a^{22}\times \frac{1}{4})$$

Whakareatia te \frac{1}{16} ki te \frac{1}{4}, ka \frac{1}{64}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{64}a^{22})$$

Ko te pārōnaki o ax^{n} ko nax^{n-1}.

$$22\times \frac{1}{64}a^{22-1}$$

Whakareatia 22 ki te \frac{1}{64}.

$$\frac{11}{32}a^{22-1}$$

Tango 1 mai i 22.

$$\frac{11}{32}a^{21}$$