Resolver (81/16)^{0.25}*((-8)^-frac{4{3}}*a^-8)*(2^-2*a^30)=

$$( \frac { 81 } { 16 } ) ^ { 0.25 } \cdot ( ( - 8 ) ^ { - \frac { 4 } { 3 } } \cdot a ^ { - 8 } ) \cdot ( 2 ^ { - 2 } \cdot a ^ { 30 } ) =$$

Calcular

$$\frac{3a^{22}}{128}$$

Pasos da solución

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

$$\left(\frac{81}{16}\right)^{0.25}\left(-8\right)^{-\frac{4}{3}}a^{22}\times 2^{-2}$$

Calcula \frac{81}{16} á potencia de 0.25 e obtén \frac{3}{2}.

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

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

$$\frac{3}{2}\times \frac{1}{16}a^{22}\times 2^{-2}$$

Multiplica \frac{3}{2} e \frac{1}{16} para obter \frac{3}{32}.

$$\frac{3}{32}a^{22}\times 2^{-2}$$

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

$$\frac{3}{32}a^{22}\times \frac{1}{4}$$

Multiplica \frac{3}{32} e \frac{1}{4} para obter \frac{3}{128}.

$$\frac{3}{128}a^{22}$$

Diferenciar w.r.t. a

$$\frac{33a^{21}}{64}$$

Pasos que usan a definición dunha derivada

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(\frac{81}{16}\right)^{0.25}\left(-8\right)^{-\frac{4}{3}}a^{22}\times 2^{-2})$$

Calcula \frac{81}{16} á potencia de 0.25 e obtén \frac{3}{2}.

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

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3}{2}\times \frac{1}{16}a^{22}\times 2^{-2})$$

Multiplica \frac{3}{2} e \frac{1}{16} para obter \frac{3}{32}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3}{32}a^{22}\times 2^{-2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3}{32}a^{22}\times \frac{1}{4})$$

Multiplica \frac{3}{32} e \frac{1}{4} para obter \frac{3}{128}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3}{128}a^{22})$$

A derivada de ax^{n} é nax^{n-1}.

$$22\times \frac{3}{128}a^{22-1}$$

Multiplica 22 por \frac{3}{128}.

$$\frac{33}{64}a^{22-1}$$

Resta 1 de 22.

$$\frac{33}{64}a^{21}$$