(5^{-3})^{-2}*(2^{4}*5^7)div(2^2*5^2)^5 eching

$$( 5 ^ { - 3 } ) ^ { - 2 } \cdot ( 2 ^ { 4 } \cdot 5 ^ { 7 } ) \div ( 2 ^ { 2 } \cdot 5 ^ { 2 } ) ^ { 5 }$$

Baholash

$$\frac{125}{64}=1,953125$$

Yechim qadamlari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -3 va -2 ni ko‘paytirib, 6 ni oling.

$$\frac{5^{6}\times 2^{4}\times 5^{7}}{\left(2^{2}\times 5^{2}\right)^{5}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 6 va 7 ni qo‘shib, 13 ni oling.

$$\frac{5^{13}\times 2^{4}}{\left(2^{2}\times 5^{2}\right)^{5}}$$

13 daraja ko‘rsatkichini 5 ga hisoblang va 1220703125 ni qiymatni oling.

$$\frac{1220703125\times 2^{4}}{\left(2^{2}\times 5^{2}\right)^{5}}$$

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

$$\frac{1220703125\times 16}{\left(2^{2}\times 5^{2}\right)^{5}}$$

19531250000 hosil qilish uchun 1220703125 va 16 ni ko'paytirish.

$$\frac{19531250000}{\left(2^{2}\times 5^{2}\right)^{5}}$$

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

$$\frac{19531250000}{\left(4\times 5^{2}\right)^{5}}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$\frac{19531250000}{\left(4\times 25\right)^{5}}$$

100 hosil qilish uchun 4 va 25 ni ko'paytirish.

$$\frac{19531250000}{100^{5}}$$

5 daraja ko‘rsatkichini 100 ga hisoblang va 10000000000 ni qiymatni oling.

$$\frac{19531250000}{10000000000}$$

\frac{19531250000}{10000000000} ulushini 156250000 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{125}{64}$$

Omil

$$\frac{5 ^ {3}}{2 ^ {6}} = 1\frac{61}{64} = 1,953125$$