(5^{-1})^{-2}*(2^{4}*5^7)div(2^2*5^2^5) eching

$$( 5 ^ { - 1 } ) ^ { - 2 } \times ( 2 ^ { 4 } \cdot 5 ^ { 7 } ) \div ( 2 ^ { 2 } \cdot 5 ^ { 2 ^ { 5 } } )$$

Baholash

$$\frac{4}{11920928955078125}=3,3554432 \cdot 10^{-16}$$

Yechim qadamlari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -1 va -2 ni ko‘paytirib, 2 ni oling.

$$\frac{5^{2}\times 2^{4}\times 5^{7}}{2^{2}\times 5^{2^{5}}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 7 ni qo‘shib, 9 ni oling.

$$\frac{5^{9}\times 2^{4}}{2^{2}\times 5^{2^{5}}}$$

Surat va maxrajdagi ikkala 2^{2} ni qisqartiring.

$$\frac{2^{2}\times 5^{9}}{5^{2^{5}}}$$

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

$$\frac{4\times 5^{9}}{5^{2^{5}}}$$

9 daraja ko‘rsatkichini 5 ga hisoblang va 1953125 ni qiymatni oling.

$$\frac{4\times 1953125}{5^{2^{5}}}$$

7812500 hosil qilish uchun 4 va 1953125 ni ko'paytirish.

$$\frac{7812500}{5^{2^{5}}}$$

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

$$\frac{7812500}{5^{32}}$$

32 daraja ko‘rsatkichini 5 ga hisoblang va 23283064365386962890625 ni qiymatni oling.

$$\frac{7812500}{23283064365386962890625}$$

\frac{7812500}{23283064365386962890625} ulushini 1953125 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{4}{11920928955078125}$$

Omil

$$\frac{2 ^ {2}}{5 ^ {23}} = 3,3554432000000003 \times 10^{-16}$$