[(15div5)^{4}]^{3}:[(2^{2}*5*3):12*2^5:2^4]^10-1^3 eching

$$[ ( 15 \div 5 ) ^ { 4 } ] ^ { 3 } : [ ( 2 ^ { 2 } \times 5 \times 3 ) : 12 \cdot 2 ^ { 5 } : 2 ^ { 4 } ] ^ { 10 } - 1 ^ { 3 }$$

Baholash

$$-\frac{9999468559}{10000000000}\approx -0,999946856$$

Yechim qadamlari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 4 va 3 ni ko‘paytirib, 12 ni oling.

$$\frac{\left(\frac{15}{5}\right)^{12}}{\left(\frac{\frac{2^{2}\times 5\times 3}{12}\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

3 ni olish uchun 15 ni 5 ga bo‘ling.

$$\frac{3^{12}}{\left(\frac{\frac{2^{2}\times 5\times 3}{12}\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

12 daraja ko‘rsatkichini 3 ga hisoblang va 531441 ni qiymatni oling.

$$\frac{531441}{\left(\frac{\frac{2^{2}\times 5\times 3}{12}\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$\frac{531441}{\left(\frac{\frac{4\times 5\times 3}{12}\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

20 hosil qilish uchun 4 va 5 ni ko'paytirish.

$$\frac{531441}{\left(\frac{\frac{20\times 3}{12}\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

60 hosil qilish uchun 20 va 3 ni ko'paytirish.

$$\frac{531441}{\left(\frac{\frac{60}{12}\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

5 ni olish uchun 60 ni 12 ga bo‘ling.

$$\frac{531441}{\left(\frac{5\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

5 daraja ko‘rsatkichini 2 ga hisoblang va 32 ni qiymatni oling.

$$\frac{531441}{\left(\frac{5\times 32}{2^{4}}\right)^{10}}-1^{3}$$

160 hosil qilish uchun 5 va 32 ni ko'paytirish.

$$\frac{531441}{\left(\frac{160}{2^{4}}\right)^{10}}-1^{3}$$

4 daraja ko‘rsatkichini 2 ga hisoblang va 16 ni qiymatni oling.

$$\frac{531441}{\left(\frac{160}{16}\right)^{10}}-1^{3}$$

10 ni olish uchun 160 ni 16 ga bo‘ling.

$$\frac{531441}{10^{10}}-1^{3}$$

10 daraja ko‘rsatkichini 10 ga hisoblang va 10000000000 ni qiymatni oling.

$$\frac{531441}{10000000000}-1^{3}$$

3 daraja ko‘rsatkichini 1 ga hisoblang va 1 ni qiymatni oling.

$$\frac{531441}{10000000000}-1$$

-\frac{9999468559}{10000000000} olish uchun \frac{531441}{10000000000} dan 1 ni ayirish.

$$-\frac{9999468559}{10000000000}$$

Omil

$$-\frac{9999468559}{10000000000} = -0,9999468559$$