((5/3)^3)^4/(frac{5{2})^14}= eching

$$\frac { ( ( \frac { 5 } { 3 } ) ^ { 3 } ) ^ { 4 } } { ( \frac { 5 } { 2 } ) ^ { 14 } } =$$

Baholash

$$\frac{16384}{13286025}\approx 0,001233175$$

Yechim qadamlari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 4 ni ko‘paytirib, 12 ni oling.

$$\frac{\left(\frac{5}{3}\right)^{12}}{\left(\frac{5}{2}\right)^{14}}$$

12 daraja ko‘rsatkichini \frac{5}{3} ga hisoblang va \frac{244140625}{531441} ni qiymatni oling.

$$\frac{\frac{244140625}{531441}}{\left(\frac{5}{2}\right)^{14}}$$

14 daraja ko‘rsatkichini \frac{5}{2} ga hisoblang va \frac{6103515625}{16384} ni qiymatni oling.

$$\frac{\frac{244140625}{531441}}{\frac{6103515625}{16384}}$$

\frac{244140625}{531441} ni \frac{6103515625}{16384} ga bo'lish \frac{244140625}{531441} ga k'paytirish \frac{6103515625}{16384} ga qaytarish.

$$\frac{244140625}{531441}\times \frac{16384}{6103515625}$$

\frac{16384}{13286025} hosil qilish uchun \frac{244140625}{531441} va \frac{16384}{6103515625} ni ko'paytirish.

$$\frac{16384}{13286025}$$

Omil

$$\frac{2 ^ {14}}{3 ^ {12} \cdot 5 ^ {2}} = 0,0012331754606814303$$