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

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

Calcular

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

Pasos da solución

Para multiplicar potencias da mesma base, suma os seus expoñentes. Suma -8 e 30 para obter 22.

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

Multiplica 0 e 25 para obter 0.

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

Calcula \frac{81}{16} á potencia de 0 e obtén 1.

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

Calcula -8 á potencia de -\frac{4}{3} e obtén \frac{1}{16}.

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

Multiplica 1 e \frac{1}{16} para obter \frac{1}{16}.

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

Calcula 2 á potencia de -2 e obtén \frac{1}{4}.

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

Multiplica \frac{1}{16} e \frac{1}{4} para obter \frac{1}{64}.

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

Diferenciar w.r.t. a

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

Pasos que usan a definición dunha derivada

Para multiplicar potencias da mesma base, suma os seus expoñentes. Suma -8 e 30 para obter 22.

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

Multiplica 0 e 25 para obter 0.

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

Calcula \frac{81}{16} á potencia de 0 e obtén 1.

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

Calcula -8 á potencia de -\frac{4}{3} e obtén \frac{1}{16}.

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

Multiplica 1 e \frac{1}{16} para obter \frac{1}{16}.

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

Calcula 2 á potencia de -2 e obtén \frac{1}{4}.

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

Multiplica \frac{1}{16} e \frac{1}{4} para obter \frac{1}{64}.

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

A derivada de ax^{n} é nax^{n-1}.

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

Multiplica 22 por \frac{1}{64}.

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

Resta 1 de 22.

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