[frac{((2^{3})(2^{6}))^{-2}(3^{4})^{3}(3)}{((2^{6})(2^{10}))^{-1}(3^6)(3^2)(3^5)}]^10 eching

$$[ \frac { ( ( 2 ^ { 3 } ) ( 2 ^ { 6 } ) ) ^ { - 2 } ( 3 ^ { 4 } ) ^ { 3 } ( 3 ) } { ( ( 2 ^ { 6 } ) ( 2 ^ { 10 } ) ) ^ { - 1 } ( 3 ^ { 6 } ) ( 3 ^ { 2 } ) ( 3 ^ { 5 } ) } ] ^ { 10 }$$

Baholash

$$\frac{1}{1048576}\approx 0,000000954$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 6 ni qo‘shib, 9 ni oling.

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

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 9 va -2 ni ko‘paytirib, -18 ni oling.

$$\left(\frac{2^{-18}\times \left(3^{4}\right)^{3}\times 3}{\left(2^{6}\times 2^{10}\right)^{-1}\times 3^{6}\times 3^{2}\times 3^{5}}\right)^{10}$$

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

$$\left(\frac{2^{-18}\times 3^{12}\times 3}{\left(2^{6}\times 2^{10}\right)^{-1}\times 3^{6}\times 3^{2}\times 3^{5}}\right)^{10}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 12 va 1 ni qo‘shib, 13 ni oling.

$$\left(\frac{2^{-18}\times 3^{13}}{\left(2^{6}\times 2^{10}\right)^{-1}\times 3^{6}\times 3^{2}\times 3^{5}}\right)^{10}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 6 va 10 ni qo‘shib, 16 ni oling.

$$\left(\frac{2^{-18}\times 3^{13}}{\left(2^{16}\right)^{-1}\times 3^{6}\times 3^{2}\times 3^{5}}\right)^{10}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 16 va -1 ni ko‘paytirib, -16 ni oling.

$$\left(\frac{2^{-18}\times 3^{13}}{2^{-16}\times 3^{6}\times 3^{2}\times 3^{5}}\right)^{10}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 6 va 2 ni qo‘shib, 8 ni oling.

$$\left(\frac{2^{-18}\times 3^{13}}{2^{-16}\times 3^{8}\times 3^{5}}\right)^{10}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 8 va 5 ni qo‘shib, 13 ni oling.

$$\left(\frac{2^{-18}\times 3^{13}}{2^{-16}\times 3^{13}}\right)^{10}$$

Surat va maxrajdagi ikkala 3^{13} ni qisqartiring.

$$\left(\frac{2^{-18}}{2^{-16}}\right)^{10}$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun suratning darajasini maxraj darajasiga bo‘ling.

$$\left(\frac{1}{2^{2}}\right)^{10}$$

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

$$\left(\frac{1}{4}\right)^{10}$$

10 daraja ko‘rsatkichini \frac{1}{4} ga hisoblang va \frac{1}{1048576} ni qiymatni oling.

$$\frac{1}{1048576}$$

Omil

$$\frac{1}{2 ^ {20}} = 9,5367431640625 \times 10^{-7}$$