{left(sqrt{1/9+frac{6/18}}{{left(5-23/3right)}^2}right)}^3 eching

$${ \left( \frac{ \sqrt{ \frac{ 1 }{ 9 } + \frac{ 6 }{ 18 } } }{ { \left(5- \frac{ 23 }{ 3 } \right) }^{ 2 } } \right) }^{ 3 }$$

Baholash

$$\frac{27}{32768}=0,000823975$$

Yechim qadamlari

\frac{6}{18} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\left(\frac{\sqrt{\frac{1}{9}+\frac{1}{3}}}{\left(5-\frac{23}{3}\right)^{2}}\right)^{3}$$

\frac{4}{9} olish uchun \frac{1}{9} va \frac{1}{3}'ni qo'shing.

$$\left(\frac{\sqrt{\frac{4}{9}}}{\left(5-\frac{23}{3}\right)^{2}}\right)^{3}$$

\frac{4}{9} boʻlinmasining kvadrat ildizini \frac{\sqrt{4}}{\sqrt{9}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$\left(\frac{\frac{2}{3}}{\left(5-\frac{23}{3}\right)^{2}}\right)^{3}$$

-\frac{8}{3} olish uchun 5 dan \frac{23}{3} ni ayirish.

$$\left(\frac{\frac{2}{3}}{\left(-\frac{8}{3}\right)^{2}}\right)^{3}$$

2 daraja ko‘rsatkichini -\frac{8}{3} ga hisoblang va \frac{64}{9} ni qiymatni oling.

$$\left(\frac{\frac{2}{3}}{\frac{64}{9}}\right)^{3}$$

\frac{2}{3} ni \frac{64}{9} ga bo'lish \frac{2}{3} ga k'paytirish \frac{64}{9} ga qaytarish.

$$\left(\frac{2}{3}\times \frac{9}{64}\right)^{3}$$

\frac{3}{32} hosil qilish uchun \frac{2}{3} va \frac{9}{64} ni ko'paytirish.

$$\left(\frac{3}{32}\right)^{3}$$

3 daraja ko‘rsatkichini \frac{3}{32} ga hisoblang va \frac{27}{32768} ni qiymatni oling.

$$\frac{27}{32768}$$

Omil

$$\frac{3 ^ {3}}{2 ^ {15}} = 0,000823974609375$$