Issolvi frac{(-7)^{-2}*3^{-1}*11^{-2}*a^-4}{22^-4*21^-3*a^-6}

$$\frac { ( - 7 ) ^ { - 2 } \times 3 ^ { - 1 } \times 11 ^ { - 2 } \times a ^ { - 4 } } { 22 ^ { - 4 } \times 21 ^ { - 3 } \times a ^ { - 6 } }$$

Evalwa

$$121968a^{2}$$

Passi tas-Soluzzjonijiet

Biex tiddividi l-qawwa tal-istess bażi, naqqas l-esponent tad-denominatur mill-esponent tan-numeratur.

$$\frac{\left(-7\right)^{-2}\times 11^{-2}\times \frac{1}{3}a^{2}}{21^{-3}\times 22^{-4}}$$

Ikkalkula -7 bil-power ta' -2 u tikseb \frac{1}{49}.

$$\frac{\frac{1}{49}\times 11^{-2}\times \frac{1}{3}a^{2}}{21^{-3}\times 22^{-4}}$$

Ikkalkula 11 bil-power ta' -2 u tikseb \frac{1}{121}.

$$\frac{\frac{1}{49}\times \frac{1}{121}\times \frac{1}{3}a^{2}}{21^{-3}\times 22^{-4}}$$

Immultiplika \frac{1}{49} u \frac{1}{121} biex tikseb \frac{1}{5929}.

$$\frac{\frac{1}{5929}\times \frac{1}{3}a^{2}}{21^{-3}\times 22^{-4}}$$

Immultiplika \frac{1}{5929} u \frac{1}{3} biex tikseb \frac{1}{17787}.

$$\frac{\frac{1}{17787}a^{2}}{21^{-3}\times 22^{-4}}$$

Ikkalkula 21 bil-power ta' -3 u tikseb \frac{1}{9261}.

$$\frac{\frac{1}{17787}a^{2}}{\frac{1}{9261}\times 22^{-4}}$$

Ikkalkula 22 bil-power ta' -4 u tikseb \frac{1}{234256}.

$$\frac{\frac{1}{17787}a^{2}}{\frac{1}{9261}\times \frac{1}{234256}}$$

Immultiplika \frac{1}{9261} u \frac{1}{234256} biex tikseb \frac{1}{2169444816}.

$$\frac{\frac{1}{17787}a^{2}}{\frac{1}{2169444816}}$$

Iddividi \frac{1}{17787}a^{2} b'\frac{1}{2169444816} billi timmultiplika \frac{1}{17787}a^{2} bir-reċiproku ta' \frac{1}{2169444816}.

$$\frac{1}{17787}a^{2}\times 2169444816$$

Immultiplika \frac{1}{17787} u 2169444816 biex tikseb 121968.

$$121968a^{2}$$

Iddifferenzja w.r.t. a

$$243936a$$

Passi tas-Soluzzjonijiet

Biex tiddividi l-qawwa tal-istess bażi, naqqas l-esponent tad-denominatur mill-esponent tan-numeratur.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{1}{17787}}{\frac{1}{2169444816}}a^{-4-\left(-6\right)})$$

Agħmel l-aritmetika.

$$\frac{\mathrm{d}}{\mathrm{d}a}(121968a^{2})$$

Id-derivattiva ta’ polynomial hija s-somma tad-derivattivi tat-termini tagħha. Id-derivattiva ta’ terminu kostanti hija 0. Id-derivattiva ta’ ax^{n} hijanax^{n-1}.

$$2\times 121968a^{2-1}$$

Agħmel l-aritmetika.

$$243936a^{1}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$243936a$$