frac{(2^{4}*3^6)^frac{1{2}}*sqrt[3]{8}*sqrt{81}}{16^frac{3{4}}*27^frac{1{3}}} eching

$$\frac { ( 2 ^ { 4 } \times 3 ^ { 6 } ) ^ { \frac { 1 } { 2 } } \times \sqrt[ 3 ] { 8 } \times \sqrt { 81 } } { 16 ^ { \frac { 3 } { 4 } } \times 27 ^ { \frac { 1 } { 3 } } }$$

Baholash

$$81$$

Yechim qadamlari

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

$$\frac{\left(16\times 3^{6}\right)^{\frac{1}{2}}\sqrt[3]{8}\sqrt{81}}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

6 daraja ko‘rsatkichini 3 ga hisoblang va 729 ni qiymatni oling.

$$\frac{\left(16\times 729\right)^{\frac{1}{2}}\sqrt[3]{8}\sqrt{81}}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

11664 hosil qilish uchun 16 va 729 ni ko'paytirish.

$$\frac{11664^{\frac{1}{2}}\sqrt[3]{8}\sqrt{81}}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

\frac{1}{2} daraja ko‘rsatkichini 11664 ga hisoblang va 108 ni qiymatni oling.

$$\frac{108\sqrt[3]{8}\sqrt{81}}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

\sqrt[3]{8} ni hisoblab, 2 natijasiga ega bo‘ling.

$$\frac{108\times 2\sqrt{81}}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

216 hosil qilish uchun 108 va 2 ni ko'paytirish.

$$\frac{216\sqrt{81}}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

81 ning kvadrat ildizini hisoblab, 9 natijaga ega bo‘ling.

$$\frac{216\times 9}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

1944 hosil qilish uchun 216 va 9 ni ko'paytirish.

$$\frac{1944}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

\frac{3}{4} daraja ko‘rsatkichini 16 ga hisoblang va 8 ni qiymatni oling.

$$\frac{1944}{8\times 27^{\frac{1}{3}}}$$

\frac{1}{3} daraja ko‘rsatkichini 27 ga hisoblang va 3 ni qiymatni oling.

$$\frac{1944}{8\times 3}$$

24 hosil qilish uchun 8 va 3 ni ko'paytirish.

$$\frac{1944}{24}$$

81 ni olish uchun 1944 ni 24 ga bo‘ling.

$$81$$

Omil

$$3^{4}$$