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

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

Evalwa

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

Passi tas-Soluzzjonijiet

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid -8 u 30 biex tikseb 22.

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

Ikkalkula \frac{81}{16} bil-power ta' 0.25 u tikseb \frac{3}{2}.

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

Ikkalkula -8 bil-power ta' -\frac{4}{3} u tikseb \frac{1}{16}.

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

Immultiplika \frac{3}{2} u \frac{1}{16} biex tikseb \frac{3}{32}.

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

Ikkalkula 2 bil-power ta' -2 u tikseb \frac{1}{4}.

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

Immultiplika \frac{3}{32} u \frac{1}{4} biex tikseb \frac{3}{128}.

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

Iddifferenzja w.r.t. a

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

Passi għall-Użu ta' Definizzjoni ta' Dervattiv

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid -8 u 30 biex tikseb 22.

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

Ikkalkula \frac{81}{16} bil-power ta' 0.25 u tikseb \frac{3}{2}.

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

Ikkalkula -8 bil-power ta' -\frac{4}{3} u tikseb \frac{1}{16}.

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

Immultiplika \frac{3}{2} u \frac{1}{16} biex tikseb \frac{3}{32}.

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

Ikkalkula 2 bil-power ta' -2 u tikseb \frac{1}{4}.

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

Immultiplika \frac{3}{32} u \frac{1}{4} biex tikseb \frac{3}{128}.

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

Id-derivattiv ta' ax^{n} huwa nax^{n-1}.

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

Immultiplika 22 b'\frac{3}{128}.

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

Naqqas 1 minn 22.

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