Issolvi frac{10^{5}x6^5x24}{48^2x15^4x4^3}

$$\frac { 10 ^ { 5 } x 6 ^ { 5 } x 24 } { 48 ^ { 2 } x 15 ^ { 4 } x 4 ^ { 3 } }$$

Evalwa

$$\frac{5x_{24}}{48x}$$

Passi tas-Soluzzjonijiet

Immultiplika x u x biex tikseb x^{2}.

$$\frac{10^{5}x\times 6^{5}x_{24}}{48^{2}x^{2}\times 15^{4}\times 4^{3}}$$

Annulla x fin-numeratur u d-denominatur.

$$\frac{6^{5}\times 10^{5}x_{24}}{4^{3}\times 15^{4}\times 48^{2}x}$$

Ikkalkula 6 bil-power ta' 5 u tikseb 7776.

$$\frac{7776\times 10^{5}x_{24}}{4^{3}\times 15^{4}\times 48^{2}x}$$

Ikkalkula 10 bil-power ta' 5 u tikseb 100000.

$$\frac{7776\times 100000x_{24}}{4^{3}\times 15^{4}\times 48^{2}x}$$

Immultiplika 7776 u 100000 biex tikseb 777600000.

$$\frac{777600000x_{24}}{4^{3}\times 15^{4}\times 48^{2}x}$$

Ikkalkula 4 bil-power ta' 3 u tikseb 64.

$$\frac{777600000x_{24}}{64\times 15^{4}\times 48^{2}x}$$

Ikkalkula 15 bil-power ta' 4 u tikseb 50625.

$$\frac{777600000x_{24}}{64\times 50625\times 48^{2}x}$$

Immultiplika 64 u 50625 biex tikseb 3240000.

$$\frac{777600000x_{24}}{3240000\times 48^{2}x}$$

Ikkalkula 48 bil-power ta' 2 u tikseb 2304.

$$\frac{777600000x_{24}}{3240000\times 2304x}$$

Immultiplika 3240000 u 2304 biex tikseb 7464960000.

$$\frac{777600000x_{24}}{7464960000x}$$

Annulla 155520000 fin-numeratur u d-denominatur.

$$\frac{5x_{24}}{48x}$$

Iddifferenzja w.r.t. x

$$-\frac{5x_{24}}{48x^{2}}$$

Passi tas-Soluzzjonijiet

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{777600000x_{24}}{7464960000x}x^{1-1})$$

Agħmel l-aritmetika.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x_{24}}{48x}x^{0})$$

Għal kwalunkwe numru a ħlief 0, a^{0}=1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x_{24}}{48x})$$

Id-derivattiv tat-terminu kostanti huwa 0.

$$0$$