sqrt{(frac{(10^-(frac{2{3})})^-6}{(5^-3/5)^-4})+0!} eching

$$\sqrt { ( \frac { ( 10 ^ { - ( \frac { 2 } { 3 } ) } ) ^ { - 6 } } { ( \frac { 5 ^ { - 3 } } { 5 } ) ^ { - 4 } } ) + 0 ! }$$

Baholash

$$\frac{\sqrt{244140641}}{15625}\approx 1,000000033$$

Yechim qadamlari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -\frac{2}{3} va -6 ni ko‘paytirib, 4 ni oling.

$$\sqrt{\frac{10^{4}}{\left(\frac{5^{-3}}{5}\right)^{-4}}+0!}$$

5 ni 5^{-3}\times 5^{4} sifatida qaytadan yozish. Surat va maxrajdagi ikkala 5^{-3} ni qisqartiring.

$$\sqrt{\frac{10^{4}}{\left(\frac{1}{5^{4}}\right)^{-4}}+0!}$$

4 daraja ko‘rsatkichini 10 ga hisoblang va 10000 ni qiymatni oling.

$$\sqrt{\frac{10000}{\left(\frac{1}{5^{4}}\right)^{-4}}+0!}$$

4 daraja ko‘rsatkichini 5 ga hisoblang va 625 ni qiymatni oling.

$$\sqrt{\frac{10000}{\left(\frac{1}{625}\right)^{-4}}+0!}$$

-4 daraja ko‘rsatkichini \frac{1}{625} ga hisoblang va 152587890625 ni qiymatni oling.

$$\sqrt{\frac{10000}{152587890625}+0!}$$

\frac{10000}{152587890625} ulushini 625 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\frac{16}{244140625}+0!}$$

0 ning faktoriali 1 ga teng.

$$\sqrt{\frac{16}{244140625}+1}$$

\frac{244140641}{244140625} olish uchun \frac{16}{244140625} va 1'ni qo'shing.

$$\sqrt{\frac{244140641}{244140625}}$$

\sqrt{\frac{244140641}{244140625}} boʻlinmasining kvadrat ildizini \frac{\sqrt{244140641}}{\sqrt{244140625}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{\sqrt{244140641}}{\sqrt{244140625}}$$

244140625 ning kvadrat ildizini hisoblab, 15625 natijaga ega bo‘ling.

$$\frac{\sqrt{244140641}}{15625}$$