Issolvi (4^{2})^{2}:(4^{10}:4^{9})-[(2+2^{2}*9)*3-6*3^{2}]+5^7:(2^2+1)^5-2*2^3

$$( 4 ^ { 2 } ) ^ { 2 } : ( 4 ^ { 10 } : 4 ^ { 9 } ) - [ ( 2 + 2 ^ { 2 } \times 9 ) \times 3 - 6 \times 3 ^ { 2 } ] + 5 ^ { 7 } : ( 2 ^ { 2 } + 1 ) ^ { 5 } - 2 \times 2 ^ { 3 }$$

Evalwa

$$13$$

Passi tas-Soluzzjonijiet

Biex tgħolli l-qawwa ta' numru għal qawwa oħra, immultiplika l-esponenti. Immultiplika 2 u 2 biex tikseb 4.

$$\frac{4^{4}}{\frac{4^{10}}{4^{9}}}-\left(\left(2+2^{2}\times 9\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2\times 2^{3}$$

Biex tiddividi l-qawwa tal-istess bażi, naqqas l-esponent tad-denominatur mill-esponent tan-numeratur. Naqas 9 minn 10 biex tikseb 1.

$$\frac{4^{4}}{4^{1}}-\left(\left(2+2^{2}\times 9\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2\times 2^{3}$$

Biex tiddividi l-qawwa tal-istess bażi, naqqas l-esponent tad-denominatur mill-esponent tan-numeratur. Naqas 1 minn 4 biex tikseb 3.

$$4^{3}-\left(\left(2+2^{2}\times 9\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2\times 2^{3}$$

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid 1 u 3 biex tikseb 4.

$$4^{3}-\left(\left(2+2^{2}\times 9\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{4}$$

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

$$64-\left(\left(2+2^{2}\times 9\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{4}$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$64-\left(\left(2+4\times 9\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{4}$$

Immultiplika 4 u 9 biex tikseb 36.

$$64-\left(\left(2+36\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{4}$$

Żid 2 u 36 biex tikseb 38.

$$64-\left(38\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{4}$$

Immultiplika 38 u 3 biex tikseb 114.

$$64-\left(114-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{4}$$

Ikkalkula 3 bil-power ta' 2 u tikseb 9.

$$64-\left(114-6\times 9\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{4}$$

Immultiplika 6 u 9 biex tikseb 54.

$$64-\left(114-54\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{4}$$

Naqqas 54 minn 114 biex tikseb 60.

$$64-60+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{4}$$

Naqqas 60 minn 64 biex tikseb 4.

$$4+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{4}$$

Ikkalkula 5 bil-power ta' 7 u tikseb 78125.

$$4+\frac{78125}{\left(2^{2}+1\right)^{5}}-2^{4}$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$4+\frac{78125}{\left(4+1\right)^{5}}-2^{4}$$

Żid 4 u 1 biex tikseb 5.

$$4+\frac{78125}{5^{5}}-2^{4}$$

Ikkalkula 5 bil-power ta' 5 u tikseb 3125.

$$4+\frac{78125}{3125}-2^{4}$$

Iddividi 78125 b'3125 biex tikseb25.

$$4+25-2^{4}$$

Żid 4 u 25 biex tikseb 29.

$$29-2^{4}$$

Ikkalkula 2 bil-power ta' 4 u tikseb 16.

$$29-16$$

Naqqas 16 minn 29 biex tikseb 13.

$$13$$

Fattur

$$13$$