o(sqrt[3]{sqrt[3]{2^9}})^5(sqrt[6]{sqrt[3]{2^9}})^5 eching

$$o ( \sqrt[ 3 ] { \sqrt[ 3 ] { 2 ^ { 9 } } } ) ^ { 5 } ( \sqrt[ 6 ] { \sqrt[ 3 ] { 2 ^ { 9 } } } ) ^ { 5 }$$

Baholash

$$128\sqrt{2}o$$

Yechim qadamlari

9 daraja ko‘rsatkichini 2 ga hisoblang va 512 ni qiymatni oling.

$$o\left(\sqrt[3]{\sqrt[3]{512}}\right)^{5}\left(\sqrt[6]{\sqrt[3]{2^{9}}}\right)^{5}$$

\sqrt[3]{512} ni hisoblab, 8 natijasiga ega bo‘ling.

$$o\left(\sqrt[3]{8}\right)^{5}\left(\sqrt[6]{\sqrt[3]{2^{9}}}\right)^{5}$$

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

$$o\times 2^{5}\left(\sqrt[6]{\sqrt[3]{2^{9}}}\right)^{5}$$

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

$$o\times 32\left(\sqrt[6]{\sqrt[3]{2^{9}}}\right)^{5}$$

9 daraja ko‘rsatkichini 2 ga hisoblang va 512 ni qiymatni oling.

$$o\times 32\left(\sqrt[6]{\sqrt[3]{512}}\right)^{5}$$

\sqrt[3]{512} ni hisoblab, 8 natijasiga ega bo‘ling.

$$o\times 32\left(\sqrt[6]{8}\right)^{5}$$

\sqrt[6]{8} ni \sqrt[6]{2^{3}} sifatida qayta yozing. Eksponensialdan radikal shaklga oʻgiring va eksponent ichida 3 ni bekor qiling. Qayta radikal shaklga oʻgiring.

$$\sqrt[6]{8}=\sqrt[6]{2^{3}}=2^{\frac{3}{6}}=2^{\frac{1}{2}}=\sqrt{2}$$

Olingan qiymatni qayta ifodaga joylang.

$$o\times 32\left(\sqrt{2}\right)^{5}$$

o ga nisbatan hosilani topish

$$128 \sqrt{2} = 181,019335984$$