(64x^3div27a^-3)^-frac{2{3}}=? eching

$$( 64 x ^ { 3 } \div 27 a ^ { - 3 } ) ^ { - \frac { 2 } { 3 } } = ?$$

Baholash

$$\frac{9\times \left(\frac{a}{x}\right)^{2}}{16}$$

Yechim qadamlari

\frac{64x^{3}}{27}a^{-3} ni yagona kasrga aylantiring.

$$\left(\frac{64x^{3}a^{-3}}{27}\right)^{-\frac{2}{3}}$$

\frac{64x^{3}a^{-3}}{27}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\left(64x^{3}a^{-3}\right)^{-\frac{2}{3}}}{27^{-\frac{2}{3}}}$$

\left(64x^{3}a^{-3}\right)^{-\frac{2}{3}} ni kengaytirish.

$$\frac{64^{-\frac{2}{3}}\left(x^{3}\right)^{-\frac{2}{3}}\left(a^{-3}\right)^{-\frac{2}{3}}}{27^{-\frac{2}{3}}}$$

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

$$\frac{64^{-\frac{2}{3}}x^{-2}\left(a^{-3}\right)^{-\frac{2}{3}}}{27^{-\frac{2}{3}}}$$

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

$$\frac{64^{-\frac{2}{3}}x^{-2}a^{2}}{27^{-\frac{2}{3}}}$$

-\frac{2}{3} daraja ko‘rsatkichini 64 ga hisoblang va \frac{1}{16} ni qiymatni oling.

$$\frac{\frac{1}{16}x^{-2}a^{2}}{27^{-\frac{2}{3}}}$$

-\frac{2}{3} daraja ko‘rsatkichini 27 ga hisoblang va \frac{1}{9} ni qiymatni oling.

$$\frac{\frac{1}{16}x^{-2}a^{2}}{\frac{1}{9}}$$

\frac{1}{16}x^{-2}a^{2} ni \frac{1}{9} ga bo'lish \frac{1}{16}x^{-2}a^{2} ga k'paytirish \frac{1}{9} ga qaytarish.

$$\frac{1}{16}x^{-2}a^{2}\times 9$$

\frac{9}{16} hosil qilish uchun \frac{1}{16} va 9 ni ko'paytirish.

$$\frac{9}{16}x^{-2}a^{2}$$

x ga nisbatan hosilani topish

$$-\frac{9a^{2}}{8x^{3}}$$