{left(frac{8x^2{b}^-frac{1{2}}}{27x{b}^frac{3{4}}}right)}^frac{2{3}} eching

$${ \left( \frac{ 8 { x }^{ 2 } { b }^{ - \frac{ 1 }{ 2 } } }{ 27x { b }^{ \frac{ 3 }{ 4 } } } \right) }^{ \frac{ 2 }{ 3 } }$$

Baholash

$$\frac{4x^{\frac{2}{3}}}{9b^{\frac{5}{6}}}$$

Yechim qadamlari

Surat va maxrajdagi ikkala x ni qisqartiring.

$$\left(\frac{8b^{-\frac{1}{2}}x}{27b^{\frac{3}{4}}}\right)^{\frac{2}{3}}$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun suratning darajasini maxraj darajasiga bo‘ling.

$$\left(\frac{8x}{27b^{\frac{5}{4}}}\right)^{\frac{2}{3}}$$

\frac{8x}{27b^{\frac{5}{4}}}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\left(8x\right)^{\frac{2}{3}}}{\left(27b^{\frac{5}{4}}\right)^{\frac{2}{3}}}$$

\left(8x\right)^{\frac{2}{3}} ni kengaytirish.

$$\frac{8^{\frac{2}{3}}x^{\frac{2}{3}}}{\left(27b^{\frac{5}{4}}\right)^{\frac{2}{3}}}$$

\frac{2}{3} daraja ko‘rsatkichini 8 ga hisoblang va 4 ni qiymatni oling.

$$\frac{4x^{\frac{2}{3}}}{\left(27b^{\frac{5}{4}}\right)^{\frac{2}{3}}}$$

\left(27b^{\frac{5}{4}}\right)^{\frac{2}{3}} ni kengaytirish.

$$\frac{4x^{\frac{2}{3}}}{27^{\frac{2}{3}}\left(b^{\frac{5}{4}}\right)^{\frac{2}{3}}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. \frac{5}{4} va \frac{2}{3} ni ko‘paytirib, \frac{5}{6} ni oling.

$$\frac{4x^{\frac{2}{3}}}{27^{\frac{2}{3}}b^{\frac{5}{6}}}$$

\frac{2}{3} daraja ko‘rsatkichini 27 ga hisoblang va 9 ni qiymatni oling.

$$\frac{4x^{\frac{2}{3}}}{9b^{\frac{5}{6}}}$$

x ga nisbatan hosilani topish

$$\frac{8}{27\sqrt[3]{x}b^{\frac{5}{6}}}$$